Subjects -> MATHEMATICS (Total: 1118 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (819 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (819 journals)                  1 2 3 4 5 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 5)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Accounting Perspectives     Full-text available via subscription   (Followers: 9)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 17)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 9)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 44)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 13)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 8)
Advances in Complex Systems     Hybrid Journal   (Followers: 12)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 5)
Advances in Fixed Point Theory     Open Access   (Followers: 9)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 22)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 22)
Advances in Mathematical Physics     Open Access   (Followers: 10)
Advances in Mathematics     Full-text available via subscription   (Followers: 22)
Advances in Numerical Analysis     Open Access   (Followers: 8)
Advances in Operations Research     Open Access   (Followers: 14)
Advances in Operator Theory     Hybrid Journal   (Followers: 4)
Advances in Porous Media     Full-text available via subscription   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 11)
Advances in Science and Research (ASR)     Open Access   (Followers: 8)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 12)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 7)
Afrika Matematika     Hybrid Journal   (Followers: 3)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 4)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 1)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 6)
Algebra and Logic     Hybrid Journal   (Followers: 8)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 2)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 10)
American Journal of Mathematical Analysis     Open Access   (Followers: 2)
American Journal of Mathematical and Management Sciences     Hybrid Journal   (Followers: 1)
American Journal of Mathematics     Full-text available via subscription   (Followers: 9)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 13)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 10)
Analysis Mathematica     Full-text available via subscription  
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access   (Followers: 8)
Annales Mathematicae Silesianae     Open Access   (Followers: 2)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 17)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 4)
Annals of Mathematics     Full-text available via subscription   (Followers: 4)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 16)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 6)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 2)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 10)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 13)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 2)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 2)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 6)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 6)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 4)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 24)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 4)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 7)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 2)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal   (Followers: 1)
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 3)
British Journal for the History of Mathematics     Hybrid Journal  
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 15)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 3)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access   (Followers: 2)
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 23)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 6)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 3)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access   (Followers: 1)
CODEE Journal     Open Access   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 17)
Commentarii Mathematici Helvetici     Hybrid Journal  
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 4)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 5)
Complex Analysis and its Synergies     Open Access   (Followers: 3)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 11)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 3)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 1)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 10)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 11)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access   (Followers: 1)
Contributions to Discrete Mathematics     Open Access   (Followers: 1)
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access   (Followers: 1)
Demographic Research     Open Access   (Followers: 16)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access   (Followers: 3)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)

        1 2 3 4 5 | Last

Similar Journals
Journal Cover
Applied Categorical Structures
Journal Prestige (SJR): 0.49
Number of Followers: 4  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9095 - ISSN (Online) 0927-2852
Published by Springer-Verlag Homepage  [2658 journals]
  • The Construction of Braided T-Categories via
           Yetter–Drinfeld–Long Bimodules

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      Abstract: Abstract Let \(H_1\) and \(H_2\) be Hopf algebras which are not necessarily finite dimensional and \(\alpha ,\beta \in Aut_{Hopf}(H_1),\gamma ,\delta \in Aut_{Hopf}(H_2)\) . In this paper, we introduce a category \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\) , generalizing Yetter–Drinfeld–Long bimodules and construct a braided T-category \(\mathcal {LR}(H_1,H_2)\) containing all the categories \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\) as components. We also prove that if \((\alpha ,\beta ,\gamma ,\delta )\) admits a quadruple in involution, then \(_{H_1}\mathcal {LR}_{H_2}(\alpha ,\beta ,\gamma ,\delta )\) is isomorphic to the usual category \(_{H_1}\mathcal {LR}_{H_2}\) of Yetter–Drinfeld–Long bimodules.
      PubDate: 2021-12-01
       
  • Weighted limits in an $$(\infty ,1)$$ ( ∞ , 1 ) -category

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      Abstract: Abstract We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal’s approach: we identify a meaningful construction for the quasi-category of weighted cones over a diagram in a quasi-category, whose terminal object is the weighted limit of the considered diagram. We then show that each weighted limit can be expressed as an ordinary limit. When the quasi-category arises as the homotopy coherent nerve of a category enriched over Kan complexes, we generalize an argument by Riehl-Verity to show that the weighted limit agrees with the homotopy weighted limit in the sense of enriched category theory, for which explicit constructions are available. When the quasi-category is complete, tensored and cotensored over the quasi-category of spaces, we discuss a possible comparison of our definition of weighted limit with the approach by Gepner-Haugseng-Nikolaus.
      PubDate: 2021-12-01
       
  • Spectra of Tensor Triangulated Categories over a Category Algebra—A
           New Approach

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      Abstract: Abstract We provide a new method to compute the Balmer spectra of the bounded derived category and the singularity category of the category algebra of a finite EI category by a decomposition trick due to Stevenson. In particular, we reobtain the result on the singularity category given by Wang under a weaker condition.
      PubDate: 2021-12-01
       
  • Basic Concepts of Quantale-Enriched Topologies

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      Abstract: Abstract The categorical framework for our axioms of quantale-enriched topologies is the theory of modules in the monoidal category \(\textsf {Sup}\) and its free right modules generated by power sets. To express the intersection axiom we introduce the structure of a quasi-magma on a quantale. By selecting appropriate quantales and their corresponding quasi-magmas, we show that some well-established mathematical structures become quantale-enriched topologies. These include, among others, the closed left ideal lattices of non-commutative \(C^*\) algebras, lower regular function frames of approach spaces as well as quantale-valued topological spaces.
      PubDate: 2021-12-01
       
  • Idempotent Completion of n-Angulated Categories

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      Abstract: Abstract Let \({\mathcal {C}}\) be an n-angulated category. We prove that its idempotent completion \(\widetilde{{\mathcal {C}}}\) admits a unique n-angulated structure such that the canonical functor \(\iota : {\mathcal {C}}\rightarrow \widetilde{{\mathcal {C}}}\) is n-angulated. Moreover, the functor \(\iota \) induces an equivalence \(Hom _{n-ang }(\widetilde{{\mathcal {C}}},{\mathcal {D}})\cong Hom _{n-ang }({\mathcal {C}},{\mathcal {D}})\) for any idempotent complete n-angulated category \({\mathcal {D}}\) , where \(Hom _{n-ang }\) denotes the category of n-angulated functors.
      PubDate: 2021-12-01
       
  • Cartesian Differential Categories as Skew Enriched Categories

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      Abstract: Abstract We exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential categories are the same as categories with finite products enriched over this skew monoidal base. The comonad Q involved is, in fact, an example of a differential modality. Differential modalities are a kind of comonad on a symmetric monoidal k-linear category with the characteristic feature that their co-Kleisli categories are cartesian differential categories. Using our first main result, we are able to prove our second one: that every small cartesian differential category admits a full, structure-preserving embedding into the cartesian differential category induced by a differential modality (in fact, a monoidal differential modality on a monoidal closed category—thus, a model of intuitionistic differential linear logic). This resolves an important open question in this area.
      PubDate: 2021-12-01
       
  • Classifying Substructures of Extriangulated Categories via Serre
           Subcategories

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      Abstract: Abstract We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar way to the author’s classification of exact structures of a given additive category. More precisely, for an extriangulated category, possible substructures are in bijection with Serre subcategories of an abelian category consisting of defects of conflations. As a byproduct, we prove that for a given skeletally small additive category, the poset of exact structures on it is isomorphic to the poset of Serre subcategories of some abelian category.
      PubDate: 2021-12-01
       
  • Split Extensions and Actions of Bialgebras and Hopf Algebras

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      Abstract: Abstract We introduce a notion of split extension of (non-associative) bialgebras which generalizes the notion of split extension of magmas introduced by M. Gran, G. Janelidze and M. Sobral. We show that this definition is equivalent to the notion of action of (non-associative) bialgebras. We particularize this equivalence to (non-associative) Hopf algebras by defining split extensions of (non-associative) Hopf algebras and proving that they are equivalent to actions of (non-associative) Hopf algebras. Moreover, we prove the validity of the Split Short Five Lemma for these kinds of split extensions, and we examine some examples.
      PubDate: 2021-10-16
       
  • Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures

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      Abstract: Abstract This paper is a coalgebra version of Positselski (Rendiconti Seminario Matematico Univ. Padova 143: 153–225, 2020) and a sequel to Positselski (Algebras and Represent Theory 21(4):737–767, 2018). We present the definition of a pseudo-dualizing complex of bicomodules over a pair of coassociative coalgebras \({\mathcal {C}}\) and  \({\mathcal {D}}\) . For any such complex \({\mathcal {L}}^{\scriptstyle \bullet }\) , we construct a triangulated category endowed with a pair of (possibly degenerate) t-structures of the derived type, whose hearts are the abelian categories of left \({\mathcal {C}}\) -comodules and left \({\mathcal {D}}\) -contramodules. A weak version of pseudo-derived categories arising out of (co)resolving subcategories in abelian/exact categories with enough homotopy adjusted complexes is also considered. Quasi-finiteness conditions for coalgebras, comodules, and contramodules are discussed as a preliminary material.
      PubDate: 2021-10-15
       
  • Homotopies of Crossed Modules of R-Algebroids

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      Abstract: Abstract In this work, given two crossed modules \(\mathcal {M=}\left( \mu :\mathrm {M} \rightarrow \mathrm {A}\right) \) and \({\mathcal {N}}=\left( \eta :\mathrm {N} \rightarrow \mathrm {B}\right) \) of R-algebroids and a crossed module morphism \(f:{\mathcal {M}}\rightarrow {\mathcal {N}}\) , we introduce an f-derivation as an ordered pair \(H=\left( H_{1},H_{0}\right) \) of maps \(H_{1}: \mathrm {Mor}\left( \mathrm {A}\right) \rightarrow \mathrm {Mor}\left( \mathrm {N }\right) \) and \(H_{0}:\mathrm {A}_{0}\rightarrow \mathrm {Mor}\left( \mathrm {B} \right) \) which are subject to satisfy certain axioms and show that f and H determine a crossed module morphism \(g:{\mathcal {M}}\rightarrow \mathcal { N}\) . Then calling such a pair \(\left( H,f\right) \) a homotopy from f to g we prove that there exists a groupoid structure of which objects are crossed module morphisms from \({\mathcal {M}}\) to \({\mathcal {N}} \) and morphisms are homotopies between crossed module morphisms. Moreover, given two crossed module morphisms \(f,g:{\mathcal {M}}\rightarrow {\mathcal {N}}\) , we introduce an fg-map as a map \(\varLambda :\mathrm {A}_{0}\rightarrow \mathrm {Mor}\left( \mathrm {N}\right) \) subject to some conditions and then show that \(\varLambda \) determines for each homotopy \(\left( H,f\right) \) from f to g a homotopy \(\left( H^{\prime },f\right) \) from f to g. Furthermore, calling such a pair \(\left( \varLambda ,\left( H,f\right) \right) \) a 2-fold homotopy from \(\left( H,f\right) \) to \(\left( H^{\prime },f\right) \) we prove that the groupoid structure constructed by crossed module morphisms from \({\mathcal {M}}\) to \({\mathcal {N}}\) and homotopies between them is upgraded by 2-fold homotopies to a 2-groupoid structure. Besides, in order to see reduced versions of all general constructions mentioned, we examine homotopies of crossed modules of associative R-algebras, as a pre-stage.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09635-z
       
  • Subprojectivity in Abelian Categories

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      Abstract: Abstract In the last few years, López-Permouth and several collaborators have introduced a new approach in the study of the classical projectivity, injectivity and flatness of modules. This way, they introduced subprojectivity domains of modules as a tool to measure, somehow, the projectivity level of such a module (so not just to determine whether or not the module is projective). In this paper we develop a new treatment of the subprojectivity in any abelian category which shed more light on some of its various important aspects. Namely, in terms of subprojectivity, some classical results are unified and some classical rings are characterized. It is also shown that, in some categories, the subprojectivity measures notions other than the projectivity. Furthermore, this new approach allows, in addition to establishing nice generalizations of known results, to construct various new examples such as the subprojectivity domain of the class of Gorenstein projective objects, the class of semi-projective complexes and particular types of representations of a finite linear quiver. The paper ends with a study showing that the fact that a subprojectivity domain of a class coincides with its first right Ext-orthogonal class can be characterized in terms of the existence of preenvelopes and precovers.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09638-w
       
  • Universal Tensor Categories Generated by Dual Pairs

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      Abstract: Abstract Let \(V_*\otimes V\rightarrow {\mathbb {C}}\) be a non-degenerate pairing of countable-dimensional complex vector spaces V and \(V_*\) . The Mackey Lie algebra \({\mathfrak {g}}=\mathfrak {gl}^M(V,V_*)\) corresponding to this pairing consists of all endomorphisms \(\varphi \) of V for which the space \(V_*\) is stable under the dual endomorphism \(\varphi ^*: V^*\rightarrow V^*\) . We study the tensor Grothendieck category \({\mathbb {T}}\) generated by the \({\mathfrak {g}}\) -modules V, \(V_*\) and their algebraic duals \(V^*\) and \(V^*_*\) . The category \({{\mathbb {T}}}\) is an analogue of categories considered in prior literature, the main difference being that the trivial module \({\mathbb {C}}\) is no longer injective in \({\mathbb {T}}\) . We describe the injective hull I of \({\mathbb {C}}\) in \({\mathbb {T}}\) , and show that the category \({\mathbb {T}}\) is Koszul. In addition, we prove that I is endowed with a natural structure of commutative algebra. We then define another category \(_I{\mathbb {T}}\) of objects in \({\mathbb {T}}\) which are free as I-modules. Our main result is that the category \({}_I{\mathbb {T}}\) is also Koszul, and moreover that \({}_I{\mathbb {T}}\) is universal among abelian \({\mathbb {C}}\) -linear tensor categories generated by two objects X, Y with fixed subobjects \(X'\hookrightarrow X\) , \(Y'\hookrightarrow Y\) and a pairing \(X\otimes Y\rightarrow {\mathbf{1 }}\) where 1 is the monoidal unit. We conclude the paper by discussing the orthogonal and symplectic analogues of the categories \({\mathbb {T}}\) and \({}_I{\mathbb {T}}\) .
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09640-2
       
  • Differential Equations in a Tangent Category I: Complete Vector Fields,
           Flows, and Exponentials

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      Abstract: This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differential geometry, the structural analogue of a natural number object. A curve object is a preinitial object for dynamical systems; dynamical systems may, in turn, be viewed as determining systems of differential equations. The unique map from the curve object to a dynamical system is a solution of the system, and a dynamical system is said to be complete when for all initial conditions there is a solution. A subtle issue concerns the question of when a dynamical system is complete, and the paper provides abstract conditions for this. This abstract formulation also allows new perspectives on topics such as commutative vector fields and flows. In addition, the stronger notion of a differential curve object, which is the centrepiece of the last section of the paper, has exponential maps and forms a differential exponential rig. This rig then, somewhat surprisingly, has an action on every differential object and bundle in the setting. In this manner, in a very strong sense, such a curve object plays the role of the real numbers in standard differential geometry.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09629-x
       
  • Functorial Factorizations in the Category of Model Categories

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      Abstract: Abstract We prove that any right Quillen functor between arbitrary model categories admits non trivial functorial factorizations that are similar to those of a model structure. Given a monad, operad or a PROP(erad) \(\mathcal {O}\) , if we apply one of the factorizations to the forgetful functor \(\textsf {U}: \mathcal {O}{\text {-Alg}}(\textsf {M}) \longrightarrow \textsf {M}\) , we extend the theory of Quillen–Segal \(\mathcal {O}\) -algebras initiated in Bacard (Higher Struct 4(1):57–114, 2020), without the hypothesis of \(\textsf {M}\) being a combinatorial model category.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09636-y
       
  • Non-hyperoctahedral Categories of Two-Colored Partitions Part II: All
           Possible Parameter Values

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      Abstract: Abstract This article is part of a series with the aim of classifying all non-hyperoctahedral categories of two-colored partitions. Those constitute by some Tannaka-Krein type result the representation categories of a specific class of quantum groups. In Part I we introduced a class of parameters which gave rise to many new non-hyperoctahedral categories of partitions. In the present article we show that this class actually contains all possible parameter values of all non-hyperoctahedral categories of partitions. This is an important step towards the classification of all non-hyperoctahedral categories.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09641-1
       
  • Free bounded archimedean $$\ell $$ ℓ -algebras

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      Abstract: Abstract We show that free objects on sets do not exist in the category \({\varvec{ba}}\varvec{\ell }\) of bounded archimedean \(\ell \) -algebras. On the other hand, we introduce the category of weighted sets and prove that free objects on weighted sets do exist in \({\varvec{ba}}\varvec{\ell }\) . We conclude by discussing several consequences of this result.
      PubDate: 2021-10-01
      DOI: 10.1007/s10485-021-09637-x
       
  • Coends of Higher Arity

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      Abstract: Abstract We specialise a recently introduced notion of generalised dinaturality for functors \(T : (\mathcal {C}^\mathsf {op})^p \times \mathcal {C}^q \rightarrow \mathcal {D}\) to the case where the domain (resp., codomain) is constant, obtaining notions of ends (resp., coends) of higher arity, dubbed herein (p, q)-ends (resp., (p, q)-coends). While higher arity co/ends are particular instances of ‘totally symmetrised’ (ordinary) co/ends, they serve an important technical role in the study of a number of new categorical phenomena, which may be broadly classified as two new variants of category theory. The first of these, weighted category theory, consists of the study of weighted variants of the classical notions and construction found in ordinary category theory, besides that of a limit. This leads to a host of varied and rich notions, such as weighted Kan extensions, weighted adjunctions, and weighted ends. The second, diagonal category theory, proceeds in a different (albeit related) direction, in which one replaces universality with respect to natural transformations with universality with respect to dinatural transformations, mimicking the passage from limits to ends. In doing so, one again encounters a number of new interesting notions, among which one similarly finds diagonal Kan extensions, diagonal adjunctions, and diagonal ends.
      PubDate: 2021-08-30
      DOI: 10.1007/s10485-021-09653-x
       
  • Categorical Extension of Dualities: From Stone to de Vries and Beyond, I

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      Abstract: Abstract Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category KHaus of compact Hausdorff spaces and their continuous maps, as an extension of a restricted Stone duality. Then, applying a dualization of the categorical framework to the de Vries duality, we give an alternative proof of the extension of the de Vries duality to the category Tych of Tychonoff spaces that was provided by Bezhanishvili, Morandi and Olberding. In the process of doing so, we obtain new duality theorems for both categories, KHaus and Tych.
      PubDate: 2021-08-06
      DOI: 10.1007/s10485-021-09658-6
       
  • Isbell Adjunctions and Kan Adjunctions via Quantale-Enriched Two-Variable
           Adjunctions

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      Abstract: Abstract It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions constructed from suitable associated two-variable adjunctions. Representation theorems are established for fixed points of these adjunctions.
      PubDate: 2021-08-02
      DOI: 10.1007/s10485-021-09654-w
       
  • An Essential, Hyperconnected, Local Geometric Morphism that is not Locally
           Connected

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      Abstract: Abstract Thomas Streicher asked on the category theory mailing list whether every essential, hyperconnected, local geometric morphism is automatically locally connected. We show that this is not the case, by providing a counterexample.
      PubDate: 2021-08-01
      DOI: 10.1007/s10485-020-09626-6
       
 
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