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What is category theory to cognitive science? Compositional representation and comparison [PDF]
Frontiers in Psychology, 2022 Category theorists and cognitive scientists study the structural (analogical) relations between domains of interest albeit in different contexts, that is, formal and psychological systems, respectively.
Steven Phillips
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Morita theorems for functor categories [PDF]
Transactions of the American Mathematical Society, 1972 We generalize the Morita theorems to certain functor categories using properties of adjoint functors.
David C. Newell
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Quadratic functors on pointed categories [PDF]
Advances in Mathematics, 2010 64 ...
Manfred Hartl, Christine Vespa
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Derived equivalences of functor categories [PDF]
Journal of Pure and Applied Algebra, 2015 Let $\Mod \CS$ denote the category of $\CS$-modules, where $\CS$ is a small category. In the first part of this paper, we provide a version of Rickard's theorem on derived equivalence of rings for $\Mod \CS$. This will have several interesting applications.
Javad Asadollahi +2 more
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Categories with projective functors
Proceedings of the London Mathematical Society, 2005 We introduce a notion of a category with full projective functors. It encodes certain common properties of categories appearing in representation theory of Lie groups, Lie algebras and quantum groups. We describe the left or right exact functors which naturally commute with projective functors and provide a unified approach to the verification of ...
Oleksandr Khomenko
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Derived category of weak chain U-complexes [PDF]
HeliyonIn this paper, we define the derived category of weak chain U-complexes, and we give a characterization of any weak chain U-complex as an object in the right bounded homotopy category of weak chain U-complexes of projective modules.
Fajar Yuliawan +3 more
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Calculus of functors and model categories
Advances in Mathematics, 2007 22 pages. Exposition is substantially improved.
Georg Biedermann +2 more
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, 2006 In this paper, we define the functor category Fquad associated to vector spaces over the field with two elements, F\_2, equipped with a quadratic form. We show the existence of a fully-faithful, exact functor : \F \to Fquad, which preserves simple objects, where \F is the category of functors from the category of finite dimensional F\_2-vector spaces
Christine Vespa
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Direct Limit of Krasner (m, n)-Hyperrings [PDF]
Journal of Sciences, Islamic Republic of Iran, 2020 The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings.
Reza Ameri, Ameneh Asadi
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Pure and Applied Mathematics, 1970 In Chapter I we discussed various algebraic structures (rings, abelian groups, modules) and their appropriate transformations (homomorphisms). We also saw how certain constructions (for example, the formation of HomΛ(A, B) for given Λ-modules A, B) produced new structures out of given structures.
Peter Hilton +2 more
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