Subjects -> MATHEMATICS (Total: 1082 journals)
    - APPLIED MATHEMATICS (86 journals)
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    - MATHEMATICS (800 journals)
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    - PROBABILITIES AND MATH STATISTICS (106 journals)

MATHEMATICS (800 journals)                  1 2 3 4 | 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: 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: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 39)
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: 12)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 23)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 19)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 11)
Advances in Materials Science     Open Access   (Followers: 19)
Advances in Mathematical Physics     Open Access   (Followers: 8)
Advances in Mathematics     Full-text available via subscription   (Followers: 17)
Advances in Nonlinear Analysis     Open Access   (Followers: 1)
Advances in Numerical Analysis     Open Access   (Followers: 9)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal   (Followers: 2)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 10)
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: 9)
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: 3)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
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: 7)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 12)
Algorithms Research     Open Access   (Followers: 1)
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: 7)
American Journal of Operations Research     Open Access   (Followers: 8)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 6)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 5)
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: 4)
Annals of Data Science     Hybrid Journal   (Followers: 13)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 8)
Annals of Functional Analysis     Hybrid Journal   (Followers: 1)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 14)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
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  
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: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics     Open Access   (Followers: 8)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 10)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 4)
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: 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: 3)
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: 25)
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   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 3)
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: 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: 5)
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: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 19)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
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: 2)
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: 1)
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: 22)
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: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
Chaos, Solitons & Fractals : X     Open Access  
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   (Followers: 1)
Clean Air Journal     Full-text available via subscription   (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: 15)
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: 4)
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: 9)
Compositio Mathematica     Full-text available via subscription  
Comptes Rendus Mathematique     Full-text available via subscription  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 4)
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: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
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: 11)
Concrete Operators     Open Access   (Followers: 4)
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: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 15)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Desimal : Jurnal Matematika     Open Access   (Followers: 2)

        1 2 3 4 | 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  [2626 journals]
  • A Unified Classification Theorem for Mal’tsev-Like Categories
    • Abstract: Abstract In this paper we give unified characterizations of categories defined by variations of the Mal’tsev property.
      PubDate: 2020-04-01
       
  • The Universal Property of Infinite Direct Sums in $$\hbox {C}^*$$C∗
           -Categories and $$\hbox {W}^*$$W∗ -Categories
    • Abstract: Abstract When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special case of \(\hbox {C}^*\)-categories, provided that one uses enrichment in Banach spaces. We then formulate such a universal property for infinite direct sums in \(\hbox {C}^*\)-categories, and prove the equivalence with the existing definition due to Ghez, Lima and Roberts in the case of \(\hbox {W}^*\)-categories. These infinite direct sums specialize to the usual ones in the category of Hilbert spaces, and more generally in any \(\hbox {W}^*\)-category of normal representations of a \(\hbox {W}^*\)-algebra. Finding a universal property for the more general case of direct integrals remains an open problem.
      PubDate: 2020-04-01
       
  • Algebraic Theories and Commutativity in a Sheaf Topos
    • Abstract: Abstract For any site of definition \(\mathcal {C}\) of a Grothendieck topos \(\mathcal {E}\), we define a notion of a \(\mathcal {C}\)-ary Lawvere theory \(\tau : \mathscr {C} \rightarrow \mathscr {T}\) whose category of models is a stack over \(\mathcal {E}\). Our definitions coincide with Lawvere’s finitary theories when \(\mathcal {C}=\aleph _0\) and \(\mathcal {E} = {{\,\mathrm{\mathbf {Set}}\,}}\). We construct a fibered category \({{\,\mathrm{\mathbf {Mod}}\,}}^{\mathscr {T}}\) of models as a stack over \(\mathcal {E}\) and prove that it is \(\mathcal {E}\)-complete and \(\mathcal {E}\)-cocomplete. We show that there is a free-forget adjunction \(F \dashv U: {{\,\mathrm{\mathbf {Mod}}\,}}^{\mathscr {T}} \leftrightarrows \mathscr {E}\). If \(\tau \) is a commutative theory in a certain sense, then we obtain a “locally monoidal closed” structure on the category of models, which enhances the free-forget adjunction to an adjunction of symmetric monoidal \(\mathcal {E}\)-categories. Our results give a general recipe for constructing a monoidal \(\mathcal {E}\)-cosmos in which one can do enriched \(\mathcal {E}\)-category theory. As an application, we describe a convenient category of linear spaces generated by the theory of Lebesgue integration.
      PubDate: 2020-04-01
       
  • Differential Categories Revisited
    • Abstract: Abstract Differential categories were introduced to provide a minimal categorical doctrine for differential linear logic. Here we revisit the formalism and, in particular, examine the two different approaches to defining differentiation which were introduced. The basic approach used a deriving transformation, while a more refined approach, in the presence of a bialgebra modality, used a codereliction. The latter approach is particularly relevant to linear logic settings, where the coalgebra modality is monoidal and the Seely isomorphisms give rise to a bialgebra modality. Here, we prove that these apparently distinct notions of differentiation, in the presence of a monoidal coalgebra modality, are completely equivalent. Thus, for linear logic settings, there is only one notion of differentiation. This paper also presents a number of separating examples for coalgebra modalities including examples which are and are not monoidal, as well as examples which do and do not support differential structure. Of particular interest is the observation that—somewhat counter-intuitively—differential algebras never induce a differential category although they provide a monoidal coalgebra modality. On the other hand, Rota–Baxter algebras—which are usually associated with integration—provide an example of a differential category which has a non-monoidal coalgebra modality.
      PubDate: 2020-04-01
       
  • Further Results on the Structure of (Co)Ends in Finite Tensor Categories
    • Abstract: Abstract Let \({\mathcal {C}}\) be a finite tensor category, and let \({\mathcal {M}}\) be an exact left \({\mathcal {C}}\)-module category. The action of \({\mathcal {C}}\) on \({\mathcal {M}}\) induces a functor \(\rho : {\mathcal {C}} \rightarrow \mathrm {Rex}({\mathcal {M}})\), where \(\mathrm {Rex}({\mathcal {M}})\) is the category of k-linear right exact endofunctors on \({\mathcal {M}}\). Our key observation is that \(\rho \) has a right adjoint \(\rho ^{\mathrm {ra}}\) given by the end $$\begin{aligned} \rho ^{\mathrm {ra}}(F) = \int _{M \in {\mathcal {M}}} \underline{\mathrm {Hom}}(M, F(M)) \quad (F \in \mathrm {Rex}({\mathcal {M}})). \end{aligned}$$As an application, we establish the following results: (1) We give a description of the composition of the induction functor \({\mathcal {C}}_{{\mathcal {M}}}^* \rightarrow {\mathcal {Z}}({\mathcal {C}}_{{\mathcal {M}}}^*)\) and Schauenburg’s equivalence \({\mathcal {Z}}({\mathcal {C}}_{{\mathcal {M}}}^*) \approx {\mathcal {Z}}({\mathcal {C}})\). (2) We introduce the space \(\mathrm {CF}({\mathcal {M}})\) of ‘class functions’ of \({\mathcal {M}}\) and initiate the character theory for pivotal module categories. (3) We introduce a filtration for \(\mathrm {CF}({\mathcal {M}})\) and discuss its relation with some ring-theoretic notions, such as the Reynolds ideal and its generalizations. (4) We show that \(\mathrm {Ext}_{{\mathcal {C}}}^{\bullet }(1, \rho ^{\mathrm {ra}}(\mathrm {id}_{{\mathcal {M}}}))\) is isomorphic to the Hochschild cohomology of \({\mathcal {M}}\). As an application, we show that the modular group acts projectively on the Hochschild cohomology of a modular tensor category.
      PubDate: 2020-04-01
       
  • The Vietoris Monad and Weak Distributive Laws
    • Abstract: Abstract The Vietoris monad on the category of compact Hausdorff spaces is a topological analogue of the power-set monad on the category of sets. Exploiting Manes’ characterisation of the compact Hausdorff spaces as algebras for the ultrafilter monad on sets, we give precise form to the above analogy by exhibiting the Vietoris monad as induced by a weak distributive law, in the sense of Böhm, of the power-set monad over the ultrafilter monad.
      PubDate: 2020-04-01
       
  • Exact Filters and Joins of Closed Sublocales
    • Abstract: Abstract We prove, for a general frame, that the sublocales that can be represented as joins of closed ones are, somewhat surprisingly, in a natural one-to-one correspondence with the filters closed under exact meets, and explain some subfit facts from this perspective. Furthermore we discuss the filters associated in a similar vein with the fitted sublocales.
      PubDate: 2020-03-07
       
  • A Topological Groupoid Representing the Topos of Presheaves on a Monoid
    • Abstract: Abstract Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos of presheaves on an arbitrary monoid. If the monoid is embeddable in a group, the resulting topological groupoid is the action groupoid for a discrete group acting on a topological space. For these monoids, we show how to compute the points of the associated topos.
      PubDate: 2020-03-06
       
  • Recognizing Quasi-Categorical Limits and Colimits in Homotopy Coherent
           Nerves
    • Abstract: Abstract In this paper we prove that various quasi-categories whose objects are \(\infty \)-categories in a very general sense are complete: admitting limits indexed by all simplicial sets. This result and others of a similar flavor follow from a general theorem in which we characterize the data that is required to define a limit cone in a quasi-category constructed as a homotopy coherent nerve. Since all quasi-categories arise this way up to equivalence, this analysis covers the general case. Namely, we show that quasi-categorical limit cones may be modeled at the point-set level by pseudo homotopy limit cones, whose shape is governed by the weight for pseudo limits over a homotopy coherent diagram but with the defining universal property up to equivalence, rather than isomorphism, of mapping spaces. Our applications follow from the fact that the \((\infty ,1)\)-categorical core of an \(\infty \)-cosmos admits weighted homotopy limits for all flexible weights, which includes in particular the weight for pseudo cones.
      PubDate: 2020-03-06
       
  • Universal Central Extensions of Internal Crossed Modules via the
           Non-abelian Tensor Product
    • Abstract: Abstract In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a universal central extension. This extends results of Brown and Loday (Topology 26(3):311–335, 1987, in the case of groups) and Edalatzadeh (Appl Categ Struct 27(2):111–123, 2019, in the case of Lie algebras). Our aim is to explain how those results can be understood in terms of categorical Galois theory: Edalatzadeh’s interpretation in terms of quasi-pointed categories applies, but a more straightforward approach based on the theory developed in a pointed setting by Casas and Van der Linden (Appl Categ Struct 22(1):253–268, 2014) works as well.
      PubDate: 2020-03-02
       
  • Crossed Modules of Monoids II: Relative Crossed Modules
    • Abstract: Abstract This is the second part of a series of three strongly related papers in which three equivalent structures are studied:Internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans.Crossed modules of monoids relative to this class of spans.Simplicial monoids of so-called Moore length 1 relative to this class of spans. The most important examples of monoids that are covered are small categories (treated as monoids in categories of spans) and bimonoids in symmetric monoidal categories (regarded as monoids in categories of comonoids). In this second part we define relative crossed modules of monoids and prove their equivalence with the relative categories of Part I.
      PubDate: 2020-02-27
       
  • Extensions of Filtered Ogus Structures
    • Abstract: Abstract We compute the Ext group of the (filtered) Ogus category over a number field K. In particular we prove that the filtered Ogus realisation of mixed motives is not fully faithful.
      PubDate: 2020-02-01
       
  • Local Presentability of Certain Comma Categories
    • Abstract: Abstract It follows from standard results that if \(\mathcal {A}\) and \(\mathcal {C}\) are locally \(\lambda \)-presentable categories and \(F : \mathcal {A}\rightarrow \mathcal {C}\) is a \(\lambda \)-accessible functor, then the comma category \(\mathsf {Id}_\mathcal {C}{\downarrow }{}F\) is locally \(\lambda \)-presentable. We show that, under the same hypotheses, \(F{\downarrow }{}\mathsf {Id}_\mathcal {C}\) is also locally \(\lambda \)-presentable.
      PubDate: 2020-02-01
       
  • On Integral Structure Types
    • Abstract: Abstract We introduce integral structure types as a categorical analogue of virtual combinatorial species. Integral structure types then categorify power series with possibly negative coefficients in the same way that combinatorial species categorify power series with non-negative rational coefficients. The notion of an operator on combinatorial species naturally extends to integral structure types, and in light of their ‘negativity’ we define the notion of the commutator of two operators on integral structure types. We then extend integral structure types to the setting of stuff types as introduced by Baez and Dolan, and then conclude by using integral structure types to give a combinatorial description for Chern classes of projective hypersurfaces.
      PubDate: 2020-02-01
       
  • Categorified Cyclic Operads
    • Abstract: Abstract In this paper, we introduce a notion of categorified cyclic operad for set-based cyclic operads with symmetries. Our categorification is obtained by relaxing defining axioms of cyclic operads to isomorphisms and by formulating coherence conditions for these isomorphisms. The coherence theorem that we prove has the form “all diagrams of canonical isomorphisms commute”. Our coherence results come in two flavours, corresponding to the “entries-only” and “exchangeable-output” definitions of cyclic operads. Our proof of coherence in the entries-only style is of syntactic nature and relies on the coherence of categorified non-symmetric operads established by Došen and Petrić. We obtain the coherence in the exchangeable-output style by “lifting” the equivalence between entries-only and exchangeable-output cyclic operads, set up by the second author. Finally, we show that a generalization of the structure of profunctors of Bénabou provides an example of categorified cyclic operad, and we exploit the coherence of categorified cyclic operads in proving that the Feynman category for cyclic operads, due to Kaufmann and Ward, admits an odd version.
      PubDate: 2020-02-01
       
  • Characterizations of Majority Categories
    • Abstract: Abstract In universal algebra, it is well known that varieties admitting a majority term admit several Mal’tsev-type characterizations. The main aim of this paper is to establish categorical counterparts of some of these characterizations for regular categories. We prove a categorical version of Bergman’s Double-projection Theorem: a regular category is a majority category if and only if every subobject S of a finite product \(A_1 \times A_2 \times \cdots \times A_n\) is uniquely determined by its twofold projections. We also establish a categorical counterpart of the Pairwise Chinese Remainder Theorem for algebras, and characterize regular majority categories by the classical congruence equation \(\alpha \cap (\beta \circ \gamma ) = (\alpha \cap \beta ) \circ (\alpha \cap \gamma )\) due to A.F. Pixley.
      PubDate: 2020-02-01
       
  • Dynamical Systems and Sheaves
    • Abstract: Abstract A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as ‘machines’ with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special cases include continuous and discrete dynamical systems (e.g. Moore machines). Additionally, morphisms between the different types of systems allow their translation in a common framework. A central goal is to understand the systems that result from arbitrary interconnection of component subsystems, possibly of different types, as well as establish conditions that ensure totality and determinism compositionally. The fundamental categorical tools used here include lax monoidal functors, which provide a language of compositionality, as well as sheaf theory, which flexibly captures the crucial notion of time.
      PubDate: 2020-02-01
       
  • Word operads and admissible orderings
    • Abstract: Abstract We use Giraudo’s construction of combinatorial operads from monoids to offer a conceptual explanation of the origins of Hoffbeck’s path sequences of shuffle trees, and use it to define new monomial orders of shuffle trees. One such order is utilised to exhibit a quadratic Gröbner basis of the Poisson operad.
      PubDate: 2020-01-18
       
  • Compactly Generated Spaces and Quasi-spaces in Topology
    • Abstract: Abstract The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category \(\textsf {Top}\) of topological spaces and continuous functions, to study compactly generated spaces and quasi-spaces in this setting. Moreover, for a class \(\mathcal {C}\) of objects we generalize the notion of \(\mathcal {C}\)-generated spaces, from which we derive, for instance, a general concept of Alexandroff spaces. Furthermore, as done for \(\textsf {Top}\), we also study, in our level of generality, the relationship between compactly generated spaces and quasi-spaces.
      PubDate: 2020-01-18
       
  • Abelian Categories Arising from Cluster Tilting Subcategories
    • Abstract: Abstract For a triangulated category \({\mathcal {T}}\), if \({\mathcal {C}}\) is a cluster-tilting subcategory of \({\mathcal {T}}\), then the factor category \({\mathcal {T}}{/}{\mathcal {C}}\) is an abelian category. Under certain conditions, the converse also holds. This is a very important result of cluster-tilting theory, due to Koenig–Zhu and Beligiannis. Now let \({\mathcal {B}}\) be a suitable extriangulated category, which is a simultaneous generalization of triangulated categories and exact categories. We introduce the notion of pre-cluster tilting subcategory \({\mathcal {C}}\) of \({\mathcal {B}}\), which is a generalization of cluster tilting subcategory. We show that \({\mathcal {C}}\) is cluster tilting if and only if the factor category \({\mathcal {B}}{/}{\mathcal {C}}\) is abelian. Our result generalizes the related results on a triangulated category and is new for an exact category case.
      PubDate: 2020-01-03
       
 
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