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  Subjects -> MATHEMATICS (Total: 1041 journals)
    - APPLIED MATHEMATICS (84 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (770 journals)
    - MATHEMATICS (GENERAL) (43 journals)
    - NUMERICAL ANALYSIS (23 journals)
    - PROBABILITIES AND MATH STATISTICS (98 journals)

MATHEMATICS (770 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: 38)
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: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 21)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 8)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 18)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 10)
Advances in Materials Science     Open Access   (Followers: 17)
Advances in Mathematical Physics     Open Access   (Followers: 7)
Advances in Mathematics     Full-text available via subscription   (Followers: 15)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
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: 8)
Advances in Pure Mathematics     Open Access   (Followers: 9)
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: 7)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 13)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 2)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
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: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 8)
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: 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: 3)
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: 7)
Annals of Mathematics     Full-text available via subscription   (Followers: 2)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
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: 1)
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: 2)
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-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: 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: 20)
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  
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: 20)
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  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
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 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: 10)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 11)
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: 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)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal  
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: 2)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  

        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  [2574 journals]
  • Distributive Laws via Admissibility
    • Abstract: This paper concerns the problem of lifting a KZ doctrine P to the 2-category of pseudo T-algebras for some pseudomonad T. Here we show that this problem is equivalent to giving a pseudo-distributive law (meaning that the lifted pseudomonad is automatically KZ), and that such distributive laws may be simply described algebraically and are essentially unique [as known to be the case in the (co)KZ over KZ setting]. Moreover, we give a simple description of these distributive laws using Bunge and Funk’s notion of admissible morphisms for a KZ doctrine (the principal goal of this paper). We then go on to show that the 2-category of KZ doctrines on a 2-category is biequivalent to a poset. We will also discuss here the problem of lifting a locally fully faithful KZ doctrine, which we noted earlier enjoys most of the axioms of a Yoneda structure, and show that a bijection between oplax and lax structures is exhibited on the lifted “Yoneda structure” similar to Kelly’s doctrinal adjunction. We also briefly discuss how this bijection may be viewed as a coherence result for oplax functors out of the bicategories of spans and polynomials, but leave the details for a future paper.
      PubDate: 2019-12-01
       
  • Extracting a $$\Sigma $$ Σ -Mal’tsev ( $$\Sigma $$ Σ -Protomodular)
           Structure from a Mal’tsev (Protomodular) Subcategory
    • Abstract: We give conditions on an inclusion \({\mathbb {C}}\hookrightarrow {\mathbb {D}}\) where \({\mathbb {C}}\) is a Mal’tsev (resp. protomodular) subcategory in order to produce on \({\mathbb {D}}\) a partial \(\Sigma \) -Mal’tsev (resp. \(\Sigma \) -protomodular) structure.
      PubDate: 2019-12-01
       
  • Functors and Morphisms Determined by Subcategories
    • Abstract: We study the existence and uniqueness of minimal right determiners in various categories. Particularly in a \({{\,\mathrm{Hom}\,}}\) -finite hereditary abelian category with enough projectives, we prove that the Auslander–Reiten–Smalø–Ringel formula of the minimal right determiner still holds. As an application, we give a formula of minimal right determiners in the category of finitely presented representations of strongly locally finite quivers.
      PubDate: 2019-10-30
       
  • Pro-compactly Finite MV-Algebras
    • Abstract: We introduce compactly finite MV-algebras and continuous MV-algebras. We also investigate pro-compactly finite MV-algebras, which are the MV-algebras that are inverse limits of systems of compactly finite MV-algebras. We obtain that continuous MV-algebras as well as pro-compactly finite MV-algebras coincide with compact Hausdorff MV-algebras. In addition, further categorical properties of compact Hausdorff MV-algebras such as co-completeness, injective objects, (co)-Hopfian objects are considered and studied.
      PubDate: 2019-10-17
       
  • The Vietoris Monad and Weak Distributive Laws
    • 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: 2019-10-16
       
  • A Unified Classification Theorem for Mal’tsev-Like Categories
    • Abstract: In this paper we give unified characterizations of categories defined by variations of the Mal’tsev property.
      PubDate: 2019-10-15
       
  • Neighbourhood Operators: Additivity, Idempotency and Convergence
    • Abstract: We define and discuss the notions of additivity and idempotency for neighbourhood and interior operators. We then propose an order-theoretic description of the notion of convergence that was introduced by D. Holgate and J. Šlapal with the help of these two properties. This will provide a rather convenient setting in which compactness and completeness can be studied via neighbourhood operators. We prove, among other things, a Frolík-type theorem with the introduction of reflecting morphisms.
      PubDate: 2019-10-11
       
  • The Universal Property of Infinite Direct Sums in $$\hbox {C}^*$$ C ∗
           -Categories and $$\hbox {W}^*$$ W ∗ -Categories
    • 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: 2019-10-08
       
  • On the Degree in Categories of Complexes of Fixed Size
    • Abstract: We consider \(\Lambda \) an artin algebra and \(n \ge 2\) . We study how to compute the left and right degrees of irreducible morphisms between complexes in a generalized standard Auslander–Reiten component of \({{\mathbf {C_n}}(\mathrm{proj}\, \Lambda )}\) with length. We give conditions under which the kernel and the cokernel of irreducible morphisms between complexes in \({\mathbf {C_n}}(\mathrm{proj}\, \Lambda )\) belong to such a category. For a finite dimensional hereditary algebra H over an algebraically closed field, we determine when an irreducible morphism has finite left (or right) degree and we give a characterization, depending on the degrees of certain irreducible morphisms, under which \({\mathbf {C_n}}(\mathrm{proj} \,H)\) is of finite type.
      PubDate: 2019-10-01
       
  • Classifying Subcategories in Quotients of Exact Categories
    • Abstract: We classify certain subcategories in quotients of exact categories. In particular, we classify the triangulated and thick subcategories of an algebraic triangulated category, i.e. the stable category of a Frobenius category.
      PubDate: 2019-10-01
       
  • Homotopical Algebra for Lie Algebroids
    • Abstract: We construct Quillen equivalent semi-model structures on the categories of dg-Lie algebroids and \(L_\infty \) -algebroids over a commutative dg-algebra in characteristic zero. This allows one to apply the usual methods of homotopical algebra to dg-Lie algebroids: for example, every Lie algebroid can be resolved by dg-Lie algebroids that arise from dg-Lie algebras, i.e. whose anchor map is zero. As an application, we show how Lie algebroid cohomology is represented by an object in the homotopy category of dg-Lie algebroids.
      PubDate: 2019-10-01
       
  • Cofibrantly Generated Lax Orthogonal Factorisation Systems
    • Abstract: The present note has three aims. First, to complement the theory of cofibrant generation of algebraic weak factorisation systems (awfss) to cover some important examples that are not locally presentable categories. Secondly, to prove that cofibrantly kz-generated awfss (a notion we define) are always lax orthogonal. Thirdly, to show that the two known methods of building lax orthogonal awfss, namely cofibrantly kz-generation and the method of “simple adjunctions”, construct different awfss. We study in some detail the example of cofibrant kz-generation that yields representable multicategories, and a counterexample to cofibrant generation provided by continuous lattices.
      PubDate: 2019-10-01
       
  • Reedy Diagrams in V-Model Categories
    • Abstract: We study the category of Reedy diagrams in a \(\mathscr {V}\) -model category. Explicitly, we show that if K is a small category, \(\mathscr {V}\) is a closed symmetric monoidal category and \(\mathscr {C}\) is a closed \(\mathscr {V}\) -module, then the diagram category \(\mathscr {V}^K\) is a closed symmetric monoidal category and the diagram category \(\mathscr {C}^K\) is a closed \(\mathscr {V}^K\) -module. We then prove that if further K is a Reedy category, \(\mathscr {V}\) is a monoidal model category and \(\mathscr {C}\) is a \(\mathscr {V}\) -model category, then with the Reedy model category structures, \(\mathscr {V}^K\) is a monoidal model category and \(\mathscr {C}^K\) is a \(\mathscr {V}^K\) -model category provided that either the unit 1 of \(\mathscr {V}\) is cofibrant or \(\mathscr {V}\) is cofibrantly generated.
      PubDate: 2019-10-01
       
  • On Integral Structure Types
    • 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: 2019-09-12
       
  • Algebraic Theories and Commutativity in a Sheaf Topos
    • 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: 2019-09-09
       
  • Further Results on the Structure of (Co)Ends in Finite Tensor Categories
    • 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: 2019-09-06
       
  • Extensions of Filtered Ogus Structures
    • 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: 2019-08-28
       
  • Maximal Lindelöf Locales
    • Abstract: For a subfit frame L, let \({\mathcal {S}}_{\mathfrak {c}}(L)\) denote the complete Boolean algebra whose elements are the sublocales of L that are joins of closed sublocales. Identifying every element of L with the open sublocale it determines allows us to view L as a subframe of \({\mathcal {S}}_{\mathfrak {c}}(L)\) . With this backdrop, we say L is maximal Lindelöf if it is Lindelöf and whenever \(L\subseteq M\) , for some Lindelöf subframe M of \({\mathcal {S}}_{\mathfrak {c}}(L)\) , then \(L=M\) . Recall that a topological space \((X,\tau )\) is maximal Lindelöf if it is Lindelöf, and there is no strictly finer topology \(\rho \) on X such that \((X,\rho )\) is a Lindelöf space. We show that a space is maximal Lindelöf if and only if the frame of its open subsets is maximal Lindelöf. We then characterize maximal Lindelöf frames internally. Among regular frames, we show that the maximal Lindelöf frames are precisely the Lindelöf ones in which every \(F_\sigma \) -sublocale (meaning a join of countably many closed sublocales) is closed.
      PubDate: 2019-08-20
       
  • Compact Hausdorff Spaces with Relations and Gleason Spaces
    • Abstract: We consider an alternate form of the equivalence between the category of compact Hausdorff spaces and continuous functions and a category formed from Gleason spaces and certain relations. This equivalence arises from the study of the projective cover of a compact Hausdorff space. This line leads us to consider the category of compact Hausdorff spaces with closed relations, and the corresponding subcategories with continuous and interior relations. Various equivalences of these categories are given extending known equivalences of the category of compact Hausdorff spaces and continuous functions with compact regular frames, de Vries algebras, and also with a category of Gleason spaces that we introduce. Study of categories of compact Hausdorff spaces with relations is of interest as a general setting to consider Gleason spaces, for connections to modal logic, as well as for the intrinsic interest in these categories.
      PubDate: 2019-08-13
       
  • Crossed Modules of Monoids I: Relative Categories
    • Abstract: This is the first 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 first part the theory of relative pullbacks is worked out leading to the definition of a relative category.
      PubDate: 2019-08-10
       
 
 
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