Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 43)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 21)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 6)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
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: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
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: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
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: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
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: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 5)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
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  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
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  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 18)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 2)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
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: 4)
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  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
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: 2)
Chinese Journal of Mathematics     Open Access  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 20)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 10)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
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  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Applied Categorical Structures
Journal Prestige (SJR): 0.49
Number of Followers: 5  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9095 - ISSN (Online) 0927-2852
Published by Springer-Verlag Homepage  [2467 journals]
  • Semantic Factorization and Descent

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      Abstract: Abstract Let \({\mathbb {A}}\) be a 2-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism p exists and is preserved by a suitable morphism, the factorization given by the lax descent object of the two-dimensional cokernel diagram of p is up to isomorphism the same as the semantic factorization of p, either one existing if the other does. The result can be seen as a counterpart account to the celebrated Bénabou–Roubaud theorem. This leads in particular to a monadicity theorem, since it characterizes monadicity via descent. It should be noted that all the conditions on the codensity monad of p trivially hold whenever p has a left adjoint and, hence, in this case, we find monadicity to be a two-dimensional exact condition on p, namely, to be an effective faithful morphism of the 2-category \({\mathbb {A}}\) .
      PubDate: 2022-11-15
       
  • Weight Structures Cogenerated by Weak Cocompact Objects

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      Abstract: Abstract We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. We also study weight structures cogenerated by sets of objects satisfying the dual condition. Under some appropriate hypothesis, it turns out that the weight structure is right adjacent to the t-structure.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09676-y
       
  • Grothendieck Enriched Categories

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      Abstract: Abstract In this paper, we introduce the notion of Grothendieck enriched categories for categories enriched over a sufficiently nice Grothendieck monoidal category \(\mathcal {V}\) , generalizing the classical notion of Grothendieck categories. Then we establish the Gabriel-Popescu type theorem for Grothendieck enriched categories. We also prove that the property of being Grothendieck enriched categories is preserved under the change of the base monoidal categories by a monoidal right adjoint functor. In particular, if we take as \(\mathcal {V}\) the monoidal category of complexes of abelian groups, we obtain the notion of Grothendieck dg categories. As an application of the main results, we see that the dg category of complexes of quasi-coherent sheaves on a quasi-compact and quasi-separated scheme is an example of Grothendieck dg categories.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09681-1
       
  • Morphisms and Pushouts in Compact Normal Joinfit Frames

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      Abstract: Abstract \(\mathfrak {KNJ}\) is the category of compact normal joinfit frames and frame homomorphisms and \(\mathfrak {KReg}\) is the coreflective subcategory of compact regular frames. This work investigates \(\mathfrak {KNJ}\) through its interaction with \(\mathfrak {KReg}\) via the coreflection \(\rho \) . A \(\mathfrak {KNJ}\) morphism \(\phi : F \longrightarrow M\) is \(\mathcal {P}\) -essential if \(\phi \) is skeletal and the map between the frames of polars, \(\mathcal {P}(\phi ): \mathcal {P}F \longrightarrow \mathcal {P}M\) defined by \(\mathcal {P}(\phi )(p)=\phi (p)^{\perp \perp }\) , is a boolean isomorphism. The \(\mathcal {P}\) -essential morphisms in \(\mathfrak {KNJ}\) are closely related to the essential embeddings in \(\mathfrak {KReg}\) . We provide a characterization of the \(\mathcal {P}\) -essential morphisms in \(\mathfrak {KNJ}\) and a connection to the essential embeddings in \(\mathfrak {KReg}\) . Further results about the preservation of joinfitness, the factorization of morphisms, and monomorphisms in \(\mathfrak {KNJ}\) are provided. Moreover, in the category of \(\mathfrak {KNJ}\) objects and skeletal frame homomorphisms, \(\mathfrak {KNJS}\) , we construct for \(F \in \mathfrak {KNJ}\) and \(\phi :\rho F \longrightarrow H\) (an arbitrary \(\mathfrak {KReg}\) essential embedding of \(\rho F\) ) the \(\mathfrak {KNJS}\) pushout of \(\rho _F: \rho F \longrightarrow F\) and \(\phi : \rho F \longrightarrow H\) . Lastly, we investigate the epimorphisms and epicomplete objects in \(\mathfrak {KNJS}\) .
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09679-9
       
  • On Continuity of Accessible Functors

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      Abstract: Abstract We prove that for each locally \(\alpha \) -presentable category \({\mathcal {K}}\) there exists a regular cardinal \(\gamma \) such that any \(\alpha \) -accessible functor out of \({\mathcal {K}}\) (into another locally \(\alpha \) -presentable category) is continuous if and only if it preserves \(\gamma \) -small limits; as a consequence we obtain a new adjoint functor theorem specific to the \(\alpha \) -accessible functors out of \({\mathcal {K}}\) . Afterwards we generalize these results to the enriched setting and deduce, among other things, that a small \({\mathcal {V}}\) -category is accessible if and only if it is Cauchy complete.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09677-x
       
  • On the Composition of Three Irreducible Morphisms in the Bounded Homotopy
           Category

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      Abstract: Abstract Let \(\Lambda \) be an artin algebra of finite global dimension. We study when the composition of three irreducible morphisms between indecomposable complexes in \({{\mathbf {K}}^{b}(\mathrm {proj}\,\Lambda )}\) is a non-zero morphism in the fourth power of the radical. We apply such results to prove that the composition of three irreducible morphisms between indecomposable complexes in the bounded derived category of a gentle Nakayama algebra, not selfinjective, whose ordinary quiver is an oriented cycle, belongs to the fourth power of the radical if and only if it vanishes.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09682-0
       
  • Projective and Reedy Model Category Structures for (Infinitesimal)
           Bimodules over an Operad

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      Abstract: Abstract We construct and study projective and Reedy model category structures for bimodules and infinitesimal bimodules over topological operads. Both model structures produce the same homotopy categories. For the model categories in question, we build explicit cofibrant and fibrant replacements. We show that these categories are right proper and under some conditions left proper. We also study the extension/restriction adjunctions.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09675-z
       
  • Relative Oppermann–Thomas Cluster Tilting Objects in $$(n+2)$$ ( n +
           2 ) -Angulated Categories

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      Abstract: Abstract Let \(\mathcal {T}\) be a k-linear Hom-finite \((n+2)\) -angulated category with n-suspension functor \(\Sigma ^n\) , split idempotents, and Serre functor \(\mathbb {S}\) . Let T be an Oppermann–Thomas cluster tilting object in \(\mathcal {T}\) with endomorphism algebra \(\Gamma = \mathrm {End}_\mathcal {T}(T)\) . We introduce the notions of relative Oppermann–Thomas cluster tilting objects and support \(\tau _n\) -tilting pairs, and show that there is an bijection between the set of isomorphism classes of basic relative Oppermann–Thomas cluster tilting objects in \(\mathcal {T}\) and the set of isomorphism classes of basic support \(\tau _n\) -tilting pairs in an n-cluster tilting subcategory of \(\mathrm {mod}~\Gamma \) . As applications, we recover the Yang–Zhu bijection (Trans Am Math Soc 371:387–412, 2019) and Adachi–Iyama–Reiten bijection (Compos Math 150:415–452, 2014), and we give a natural partial order for relative Oppermann–Thomas cluster tilting objects.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09673-1
       
  • Internal Enriched Categories

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      Abstract: Abstract We introduce the theory of enrichment over an internal monoidal category as a common generalization of both the standard theories of enriched and internal categories. Then, we contextualize the new notion by comparing it to another known generalization of enrichment: that of enrichment for indexed categories. It turns out that the two notions are closely related.
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09678-w
       
  • Maps with Discrete Fibers and the Origin of Basepoints

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      Abstract: Abstract Let \({p : \mathcal {E}\rightarrow \mathcal S}\) be a hyperconnected geometric morphism. For each X in the ‘gros’ topos \(\mathcal {E}\) , there is a hyperconnected geometric morphism \({p_X : \mathcal {E}/X \rightarrow \mathcal S(X)}\) from the slice over X to the ‘petit’ topos of maps (over X) with discrete fibers. We show that if p is essential then \(p_X\) is essential for every X. The proof involves the idea of collapsing a connected subspace to a ‘basepoint’, as in Algebraic Topology, but formulated in topos-theoretic terms. In case p is local, we characterize when \({p_X}\) is local for every X. This is a very restrictive property, typical of toposes of spaces of dimension \({\le 1}\) .
      PubDate: 2022-10-01
      DOI: 10.1007/s10485-022-09680-2
       
  • 2-Cartesian Fibrations I: A Model for $$\infty $$ -Bicategories Fibred in
           $$\infty $$ -Bicategories

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      Abstract: Abstract In this paper, we provide a notion of \(\infty \) -bicategories fibred in \(\infty \) -bicategories which we call 2-Cartesian fibrations. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled simplicial sets equipped with an additional collection of triangles containing the scaled 2-simplices, which we call lean triangles, in addition to a collection of edges containing all degenerate 1-simplices. We prove the existence of a left proper combinatorial simplicial model category whose fibrant objects are precisely the 2-Cartesian fibrations over a chosen scaled simplicial set S. Over the terminal scaled simplicial set, this provides a new model structure modeling \(\infty \) -bicategories, which we show is Quillen equivalent to Lurie’s scaled simplicial set model. We conclude by providing a characterization of 2-Cartesian fibrations over an \(\infty \) -bicategory. This characterization then allows us to identify those 2-Cartesian fibrations arising as the coherent nerve of a fibration of \({\text {Set}}^+_{\Delta }\) -enriched categories, thus showing that our definition recovers the preexisting notions of fibred 2-categories.
      PubDate: 2022-09-28
       
  • Matrix Taxonomy and Bourn Localization

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      Abstract: Abstract In a recent paper (Hoefnagel et al. in Theory Appl Categ 38:737–790, 2022), an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices—the so called ‘matrix properties’. In this paper we extend this algorithm to include matrix properties involving pointedness of a category, such as the properties of a category to be unital, strongly unital or subtractive, for example. Moreover, this extended algorithm can also be used to determine whether a given matrix property is the Bourn localization of another, thus leading to new characterizations of Mal’tsev, majority and arithmetical categories. Using a computer implementation of our algorithm, we can display all such properties given by matrices of fixed dimensions, grouped according to their Bourn localizations, as well as the implications between them.
      PubDate: 2022-09-21
       
  • 2-Limits and 2-Terminal Objects are too Different

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      Abstract: Abstract In ordinary category theory, limits are known to be equivalent to terminal objects in the slice category of cones. In this paper, we prove that the 2-categorical analogues of this theorem relating 2-limits and 2-terminal objects in the various choices of slice 2-categories of 2-cones are false. Furthermore we show that, even when weakening the 2-cones to pseudo- or lax-natural transformations, or considering bi-type limits and bi-terminal objects, there is still no such correspondence.
      PubDate: 2022-09-08
      DOI: 10.1007/s10485-022-09691-z
       
  • A Topological Duality for Monotone Expansions of Semilattices

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      Abstract: Abstract In this paper we provide a Stone style duality for monotone semilattices by using the topological duality developed in S. Celani, L.J. González (Appl Categ Struct 28:853–875, 2020) for semilattices together with a topological description of their canonical extension. As an application of this duality we obtain a characterization of the congruences of monotone semilattices by means of monotone lower-Vietoris-type topologies.
      PubDate: 2022-08-29
      DOI: 10.1007/s10485-022-09690-0
       
  • The Representation Theory of Brauer Categories I: Triangular Categories

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      Abstract: This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple complex Lie algebra, and develop a highest weight theory for them. We show that the Brauer category, the partition category, and a number of related diagram categories admit this structure.
      PubDate: 2022-08-13
      DOI: 10.1007/s10485-022-09689-7
       
  • Quotients of Span Categories that are Allegories and the Representation of
           Regular Categories

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      Abstract: Abstract We consider the ordinary category \(\mathsf {Span}({\mathcal {C}})\) of (isomorphism classes of) spans of morphisms in a category \(\mathcal {C}\) with finite limits as needed, composed horizontally via pullback, and give a general criterion for a quotient of \(\mathsf {Span}({\mathcal {C}})\) to be an allegory. In particular, when \({\mathcal {C}}\) carries a pullback-stable, but not necessarily proper, \(({\mathcal {E}},{\mathcal {M}})\) -factorization system, we establish a quotient category \(\mathsf {Span}_{{\mathcal {E}}}({\mathcal {C}})\) that is isomorphic to the category \(\mathsf {Rel}_{{\mathcal {M}}}({\mathcal {C}})\) of \({\mathcal {M}}\) -relations in \({\mathcal {C}}\) , and show that it is a (unitary and tabular) allegory precisely when \({\mathcal {M}}\) is a class of monomorphisms in \({\mathcal {C}}\) . Without the restriction to monomorphisms, one can still find a least pullback-stable and composition-closed class \({\mathcal {E}}_{\bullet }\) containing \(\mathcal E\) such that \(\mathsf {Span}_{{\mathcal {E}}_{\bullet }}({\mathcal {C}})\) is a unitary and tabular allegory. In this way one obtains a left adjoint to the 2-functor that assigns to every unitary tabular allegory the regular category of its Lawverian maps. With the Freyd-Scedrov Representation Theorem for regular categories, we conclude that every finitely complete category with a stable factorization system has a reflection into the 2-category of all regular categories.
      PubDate: 2022-08-01
      DOI: 10.1007/s10485-022-09687-9
       
  • Covariant Isotropy of Grothendieck Toposes and Extensive Categories

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      Abstract: Abstract We provide an explicit characterization of the covariant isotropy group of any Grothendieck topos, i.e. the group of (extended) inner automorphisms of any sheaf over a small site. In order to do so, we first extend previous techniques for computing covariant isotropy from locally finitely presentable categories to locally presentable categories. As a consequence, we also obtain an explicit characterization of the centre of a Grothendieck topos, i.e. the automorphism group of its identity functor. We conclude by providing a more categorical approach to show that these characterizations also extend to any extensive category.
      PubDate: 2022-08-01
      DOI: 10.1007/s10485-022-09674-0
       
  • Finite Distributive Semilattices

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      Abstract: Abstract The present article aims to develop a categorical duality for the category of finite distributive join-semilattices and \(\wedge \) -homomorphisms (maps that preserve the joins and the meets, when they exist). This dual equivalence is a generalization of the famous categorical duality given by Birkhoff for finite distributive lattices. Moreover, we show that every finite distributive semilattice is a Hilbert algebra with supremum. We obtain some applications from the dual equivalence. We provide a dual description of the 1–1 and onto \(\wedge \) -homomorphisms, and we obtain a dual characterization of some subalgebras. Finally, we present a representation for the class of finite semi-boolean algebras.
      PubDate: 2022-08-01
      DOI: 10.1007/s10485-021-09669-3
       
  • Compatibility of t-Structures in a Semiorthogonal Decomposition

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      Abstract: Abstract We describe how to obtain a global t-structure from a semiorthogonal decomposition with compatible t-structures on every component. This result is used to generalize a well-known theorem of Bondal on full strong exceptional sequences.
      PubDate: 2022-08-01
      DOI: 10.1007/s10485-022-09672-2
       
  • Kan Extensions are Partial Colimits

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      Abstract: Abstract One way of interpreting a left Kan extension is as taking a kind of “partial colimit”, whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the partial evaluations sitting in the so-called bar construction of monads. The (pseudo)monads of interest for forming colimits are the monad of diagrams and the monad of small presheaves, both on the (huge) category CAT of locally small categories. Throughout, particular care is taken to handle size issues, which are notoriously delicate in the context of free cocompletion. We spell out, with all 2-dimensional details, the structure maps of these pseudomonads. Then, based on a detailed general proof of how the restriction-of-scalars construction of monads extends to the case of pseudoalgebras over pseudomonads, we consider a morphism of monads between them, which we call image. This morphism allows in particular to generalize the idea of confinal functors, i.e. of functors which leave colimits invariant in an absolute way. This generalization includes the concept of absolute colimit as a special case. The main result of this paper spells out how a pointwise left Kan extension of a diagram corresponds precisely to a partial evaluation of its colimit. This categorical result is analogous to what happens in the case of probability monads, where a conditional expectation of a random variable corresponds to a partial evaluation of its center of mass.
      PubDate: 2022-08-01
      DOI: 10.1007/s10485-021-09671-9
       
 
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