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MATHEMATICS (711 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, 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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
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  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
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: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
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: 1)
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: 12)
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: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
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: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
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  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)

        1 2 3 4 | Last

Journal Cover
Applied Categorical Structures
Journal Prestige (SJR): 0.49
Number of Followers: 2  
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-9095 - ISSN (Online) 0927-2852
Published by Springer-Verlag Homepage  [2350 journals]
  • Monads on Higher Monoidal Categories
    • Authors: Marcelo Aguiar; Mariana Haim; Ignacio López Franco
      Pages: 413 - 458
      Abstract: We study the action of monads on categories equipped with several monoidal structures. We identify the structure and conditions that guarantee that the higher monoidal structure is inherited by the category of algebras over the monad. Monoidal monads and comonoidal monads appear as the base cases in this hierarchy. Monads acting on duoidal categories constitute the next case. We cover the general case of n-monoidal categories and discuss several naturally occurring examples in which \(n\le 3\) .
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9497-8
      Issue No: Vol. 26, No. 3 (2018)
  • More on the Functor Induced by z -Ideals
    • Authors: Oghenetega Ighedo
      Pages: 459 - 476
      Abstract: An ideal I of a commutative ring A with identity is called a z-ideal if whenever two elements of A belong to the same maximal ideals and one of the elements is in I, then so is the other. For a completely regular frame L we denote by \({{\mathrm{ZId}}}(\mathcal {R}L)\) the lattice of z-ideals of the ring \(\mathcal {R}L\) of continuous real-valued functions on L. It is a coherent frame, and it is known that \(L\mapsto {{\mathrm{ZId}}}(\mathcal {R}L)\) is the object part of a functor \(\mathsf {Z}:\mathbf {CRFrm}\rightarrow \mathbf {CohFrm}\) , where \(\mathbf {CRFrm}\) is the category of completely regular frames and frame homomorphisms, and \(\mathbf {CohFrm}\) is the category of coherent frames and coherent maps. We explore when this functor preserves and reflects the property of being a Heyting homomorphism, and also when it preserves and reflects the variants of openness of Banaschewski and Pultr (Appl Categ Struct 2:331–350, 1994). We also record some other properties of this functor that have hitherto not been stated anywhere.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9498-7
      Issue No: Vol. 26, No. 3 (2018)
  • On the Maps of Pointfree Topology Which Preserve the Rings of
           Integervalued Continuous Functions
    • Authors: B. Banaschewski
      Pages: 477 - 489
      Abstract: This paper establishes various conditions characterizing the homomorphisms \(h: L \rightarrow M\) of 0-dimensional frames which induce an isomorphism between the rings of all integervalued continuous function, or their bounded parts, on L and M, based on the Lindelöf and the compact coreflection of 0-dimensional frames. This provides natural analogues of familiar results concerning the realvalued continuous functions on completely regular frames, albeit by rather different methods of proof from those originally used in that setting. In addition, it will be shown that the present approach also leads to alternative proofs for the latter.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9499-6
      Issue No: Vol. 26, No. 3 (2018)
  • A Simultaneous Generalization of Mutation and Recollement of Cotorsion
           Pairs on a Triangulated Category
    • Authors: Hiroyuki Nakaoka
      Pages: 491 - 544
      Abstract: In this article, we introduce the notion of concentric twin cotorsion pair on a triangulated category. This notion contains the notions of t-structure, cluster tilting subcategory, co-t-structure and functorally finite rigid subcategory as examples. Moreover, a recollement of triangulated categories can be regarded as a special case of concentric twin cotorsion pair. To any concentric twin cotorsion pair, we associate a pretriangulated subquotient category. This enables us to give a simultaneous generalization of the Iyama–Yoshino reduction and the recollement of cotorsion pairs. This allows us to give a generalized mutation on cotorsion pairs defined by the concentric twin cotorsion pair.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9501-3
      Issue No: Vol. 26, No. 3 (2018)
  • Crossed Simplicial Group Categorical Nerves
    • Authors: Scott Balchin
      Pages: 545 - 558
      Abstract: We extend the notion of the nerve of a category for a small class of crossed simplicial groups, explicitly describing them using generators and relations. We do this by first considering a generalised bar construction of a group before looking at twisted versions of some of these nerves. As an application we show how we can use the twisted nerves to give equivariant versions of certain derived stacks.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9502-2
      Issue No: Vol. 26, No. 3 (2018)
  • Commutants for Enriched Algebraic Theories and Monads
    • Authors: Rory B. B. Lucyshyn-Wright
      Pages: 559 - 596
      Abstract: We define and study a notion of commutant for \(\mathscr {V}\) -enriched \({\mathscr {J}}\) -algebraic theories for a system of arities \({\mathscr {J}}\) , recovering the usual notion of commutant or centralizer of a subring as a special case alongside Wraith’s notion of commutant for Lawvere theories as well as a notion of commutant for \(\mathscr {V}\) -monads on a symmetric monoidal closed category \(\mathscr {V}\) . This entails a thorough study of commutation and Kronecker products of operations in \({\mathscr {J}}\) -theories. In view of the equivalence between \({\mathscr {J}}\) -theories and \({\mathscr {J}}\) -ary monads we reconcile this notion of commutation with Kock’s notion of commutation of cospans of monads and, in particular, the notion of commutative monad. We obtain notions of \({\mathscr {J}}\) -ary commutant and absolute commutant for \({\mathscr {J}}\) -ary monads, and we show that for finitary monads on \(\text {Set}\) the resulting notions of finitary commutant and absolute commutant coincide. We examine the relation of the notion of commutant to both the notion of codensity monad and the notion of algebraic structure in the sense of Lawvere.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9503-1
      Issue No: Vol. 26, No. 3 (2018)
  • Skew-Enriched Categories
    • Authors: Alexander Campbell
      Pages: 597 - 615
      Abstract: This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of the enriched hom-objects need not be in bijection with the morphisms of the underlying category. This is the natural setting in which to introduce the notion of locally weak comonad, which is fundamental to the theory of enriched algebraic weak factorisation systems. The equivalence, for a monoidal closed category \(\mathcal {V}\) , between tensored \(\mathcal {V}\) -categories and hommed \(\mathcal {V}\) -actegories is extended to the skew setting and easily proved by recognising both skew \(\mathcal {V}\) -categories and skew \(\mathcal {V}\) -actegories as equivalent to special kinds of skew \(\mathcal {V}\) -proactegory.
      PubDate: 2018-06-01
      DOI: 10.1007/s10485-017-9504-0
      Issue No: Vol. 26, No. 3 (2018)
  • The Category of Matroids
    • Authors: Chris Heunen; Vaia Patta
      Pages: 205 - 237
      Abstract: The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful and having a nearly full Kan extension; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial. Finally, a characterization of matroids in terms of optimality of the greedy algorithm can be rephrased in terms of limits.
      PubDate: 2018-04-01
      DOI: 10.1007/s10485-017-9490-2
      Issue No: Vol. 26, No. 2 (2018)
  • Operations on Categories of Modules are Given by Schur Functors
    • Authors: Martin Brandenburg
      Pages: 287 - 308
      Abstract: Let k be a commutative \(\mathbb {Q}\) -algebra. We study families of functors between categories of finitely generated modules which are defined for all commutative k-algebras simultaneously and are compatible with base changes. These operations turn out to be Schur functors associated to k-linear representations of symmetric groups. This result is closely related to Macdonald’s classification of polynomial functors.
      PubDate: 2018-04-01
      DOI: 10.1007/s10485-017-9494-y
      Issue No: Vol. 26, No. 2 (2018)
  • Convex Spaces, Affine Spaces, and Commutants for Algebraic Theories
    • Authors: Rory B. B. Lucyshyn-Wright
      Pages: 369 - 400
      Abstract: Certain axiomatic notions of affine space over a ring and convex space over a preordered ring are examples of the notion of \(\mathscr {T}\) -algebra for an algebraic theory \(\mathscr {T}\) in the sense of Lawvere. Herein we study the notion of commutant for Lawvere theories that was defined by Wraith and generalizes the notion of centralizer clone. We focus on the Lawvere theory of left R -affine spaces for a ring or rig R, proving that this theory can be described as a commutant of the theory of pointed right R-modules. Further, we show that for a wide class of rigs R that includes all rings, these theories are commutants of one another in the full finitary theory of R in the category of sets. We define left R -convex spaces for a preordered ring R as left affine spaces over the positive part \(R_+\) of R. We show that for any firmly archimedean preordered algebra R over the dyadic rationals, the theories of left R-convex spaces and pointed right \(R_+\) -modules are commutants of one another within the full finitary theory of \(R_+\) in the category of sets. Applied to the ring of real numbers \(\mathbb {R}\) , this result shows that the connection between convex spaces and pointed \(\mathbb {R}_+\) -modules that is implicit in the integral representation of probability measures is a perfect ‘duality’ of algebraic theories.
      PubDate: 2018-04-01
      DOI: 10.1007/s10485-017-9496-9
      Issue No: Vol. 26, No. 2 (2018)
  • A New Proof of the Nešetřil–Rödl Theorem
    • Authors: Dragan Mašulović
      Pages: 401 - 412
      Abstract: In this paper we give a new proof of the Nešetřil–Rödl Theorem, a deep result of discrete mathematics which is one of the cornerstones of the structural Ramsey theory. In contrast to the well-known proofs which employ intricate combinatorial strategies, this proof is spelled out in the language of category theory and the main result follows by applying several simple categorical constructions. The gain from the approach we present here is that, instead of giving the proof in the form of a large combinatorial construction, we can start from a few building blocks and then combine them into the final proof using general principles.
      PubDate: 2018-04-01
      DOI: 10.1007/s10485-017-9500-4
      Issue No: Vol. 26, No. 2 (2018)
  • A Formula for Codensity Monads and Density Comonads
    • Authors: Jiří Adámek; Lurdes Sousa
      Abstract: For a functor F whose codomain is a cocomplete, cowellpowered category \(\mathcal {K}\) with a generator S we prove that a codensity monad exists iff for every object s in S all natural transformations from \(\mathcal {K}(X, F-)\) to \(\mathcal {K}(s, F-)\) form a set. Moreover, the codensity monad has an explicit description using the above natural transformations. Concrete examples are presented, e.g., the codensity monad of the power-set functor \(\mathcal {P}\) assigns to every set X the set of all nonexpanding endofunctions of \(\mathcal {P}X\) . Dually, a set-valued functor F is proved to have a density comonad iff all natural transformations from \(X^F\) to \(2^F\) form a set. Moreover, that comonad assigns to X the set of all those transformations. For preimages-preserving endofunctors F of \({\mathsf {Set}}\) we prove that F has a density comonad iff F is accessible.
      PubDate: 2018-05-29
      DOI: 10.1007/s10485-018-9530-6
  • Filtered $$cA_\infty $$ c A ∞ -Categories and Functor Categories
    • Authors: Olivier De Deken; Wendy Lowen
      Abstract: We develop the basic theory of curved \(A_{\infty }\) -categories ( \(cA_{\infty }\) -categories) in a filtered setting, encompassing the frameworks of Fukaya categories (Fukaya et al. in Part I, AMS/IP studies in advanced mathematics, vol 46, American Mathematical Society, Providence, RI, 2009) and weakly curved \(A_{\infty }\) -categories in the sense of Positselski (Weakly curved \(A_\infty \) algebras over a topological local ring, 2012. arxiv:1202.2697v3). Between two \(cA_{\infty }\) -categories \(\mathfrak {a}\) and \(\mathfrak {b}\) , we introduce a \(cA_{\infty }\) -category \(\mathsf {qFun}(\mathfrak {a}, \mathfrak {b})\) of so-called \(qA_{\infty }\) -functors in which the uncurved objects are precisely the \(cA_{\infty }\) -functors from \(\mathfrak {a}\) to \(\mathfrak {b}\) . The more general \(qA_{\infty }\) -functors allow us to consider representable modules, a feature which is lost if one restricts attention to \(cA_{\infty }\) -functors. We formulate a version of the Yoneda Lemma which shows every \(cA_{\infty }\) -category to be homotopy equivalent to a curved dg category, in analogy with the uncurved situation. We also present a curved version of the bar-cobar adjunction.
      PubDate: 2018-05-28
      DOI: 10.1007/s10485-018-9526-2
  • On Fibrations Between Internal Groupoids and Their Normalizations
    • Authors: P.-A. Jacqmin; S. Mantovani; G. Metere; E. M. Vitale
      Abstract: We characterize fibrations and \(*\) -fibrations in the 2-category of internal groupoids in terms of the comparison functor from certain pullbacks to the corresponding strong homotopy pullbacks. As an application, we deduce the internal version of the Brown exact sequence for \(*\) -fibrations from the internal version of the Gabriel–Zisman exact sequence. We also analyse fibrations and \(*\) -fibrations in the category of arrows and study when the normalization functor preserves and reflects them. This analysis allows us to give a characterization of protomodular categories using strong homotopy kernels and a generalization of the Snake Lemma.
      PubDate: 2018-05-26
      DOI: 10.1007/s10485-018-9529-z
  • Correction to: Infinitary Addition, Real Numbers, and Taut Monads
    • Authors: George Janelidze; Ross Street
      Abstract: In the original publication of the article, Eq. 3.24 was published incorrectly. The corrected equation is given in this correction article. The original article has been corrected.
      PubDate: 2018-05-12
      DOI: 10.1007/s10485-018-9528-0
  • Scott Approach Distance on Metric Spaces
    • Authors: Wei Li; Dexue Zhang
      Abstract: The notion of Scott distance between points and subsets in a metric space, a metric analogy of the Scott topology on an ordered set, is introduced, making a metric space into an approach space. Basic properties of Scott distance are investigated, including its topological coreflection and its relation to injective \(T_0\) approach spaces. It is proved that the topological coreflection of the Scott distance is sandwiched between the d-Scott topology and the generalized Scott topology; and that every injective \(T_0\) approach space is a cocomplete and continuous metric space equipped with its Scott distance.
      PubDate: 2018-05-09
      DOI: 10.1007/s10485-018-9527-1
  • A Note on Colebunders–Lowen–Rosiers Monads
    • Authors: George Janelidze
      Abstract: We describe an alternative way of constructing some of the monads, recently introduced by E. Colebunders, R. Lowen, and W. Rosiers for the purposes of categorical topology.
      PubDate: 2018-05-07
      DOI: 10.1007/s10485-018-9525-3
  • Infinitary Addition, Real Numbers, and Taut Monads
    • Authors: George Janelidze; Ross Street
      Abstract: We make various observations on infinitary addition in the context of the series monoids introduced in our previous paper on real sets. In particular, we explore additional conditions on such monoids suggested by Tarski’s Arithmetic of Cardinal Algebras, and present a monad-theoretic construction that generalizes our construction of paradoxical real numbers.
      PubDate: 2018-04-18
      DOI: 10.1007/s10485-018-9524-4
  • Meet-Semilattice Congruences on a Frame
    • Authors: John Frith; Anneliese Schauerte
      Abstract: The congruence lattice of a frame has long been an object of considerable interest, not least because it turns out to be a frame itself. Perhaps more surprisingly congruence lattices of, for instance, \(\sigma \) -frames, \(\kappa \) -frames and some partial frames also turn out to be frames. The situation for congruences of a meet-semilattice is notably different. In this paper we analyze the meet-semilattice congruence lattices of arbitrary frames and compare them with the corresponding lattices of frame congruences. In the course of this, we provide a structure theorem as well as many examples and counter-examples.
      PubDate: 2018-04-13
      DOI: 10.1007/s10485-018-9521-7
  • Cowellpoweredness of Some Categories of Quasi-Uniform Spaces
    • Authors: Dikran Dikranjan; Hans-Peter A. Künzi
      Abstract: We study cowellpoweredness in the category \(\mathbf{QUnif}\) of quasi-uniform spaces and uniformly continuous maps. A full subcategory \(\mathcal{A}\) of \(\mathbf{QUnif}\) is cowellpowered when the cardinality of the codomains of any class of epimorphisms in \(\mathcal{A}\) , with a fixed common domain, is bounded. We use closure operators in the sense of Dikranjan–Giuli–Tholen which provide a convenient tool for describing the subcategories \(\mathcal{A}\) of \(\mathbf{QUnif}\) and their epimorphisms. Some of the results are obtained by using the knowledge of closure operators, epimorphisms and cowellpoweredness of subcategories of the category \(\mathbf{Top}\) of topological spaces and continuous maps. The transfer is realized by lifting these subcategories along the forgetful functor \(T{:}\mathbf{QUnif}\rightarrow \mathbf{Top}\) and studying when epimorphisms and cowellpoweredness are preserved by the lifting. In other cases closure operators of \(\mathbf{QUnif}\) are used to provide specific results for \(\mathbf{QUnif}\) that have no counterpart in \(\mathbf{Top}\) . This leads to a wealth of cowellpowered categories and a wealth of non-cowellpowered categories of quasi-uniform spaces, in contrast with the current situation in the case of the smaller category \(\mathbf{Unif}\) of uniform spaces, where no example of a non-cowellpowered subcategory is known so far. Finally, we present our main example: a non-cowellpowered full subcategory of \(\mathbf{QUnif}\) which is the intersection of two “symmetric” cowellpowered full subcategories of \(\mathbf{QUnif}\) .
      PubDate: 2018-04-07
      DOI: 10.1007/s10485-018-9523-5
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