Results 1 to 10 of about 1,637,073 (286)
Topological field theories and symmetry protected topological phases with fusion category symmetries [PDF]
Journal of High Energy Physics, 2021 Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using topological ...
Kansei Inamura
doaj +2 more sources
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
doaj +2 more sources
Tambarization of a Mackey functor and its application to the Witt-Burnside construction [PDF]
arXiv, 2010 For an arbitrary group $G$, a (semi-)Mackey functor is a pair of covariant and contravariant functors from the category of $G$-sets, and is regarded as a $G$-bivariant analog of a commutative (semi-)group. In this view, a $G$-bivariant analog of a (semi-)ring should be a (semi-)Tambara functor.
Nakaoka, Hiroyuki
arxiv +4 more sources
Quadratic functors on pointed categories [PDF]
Advances in Mathematics, 2010 64 ...
Manfred Hartl, Christine Vespa
+7 more sources
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
openalex +3 more sources
Biset functors for categories [PDF]
arXiv, 2023 We introduce the theory of biset functors defined on finite categories. Previously, biset functors have been defined on groups, and in that context they are closely related to Mackey functors. Standard examples on groups include representation rings, the Burnside ring and group cohomology.
arxiv +3 more sources
The functor category Fquad [PDF]
, 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
openalex +4 more sources
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
openalex +6 more sources
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
openalex +6 more sources
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
doaj +2 more sources