Results 11 to 20 of about 5,995,783 (336)
A category of quantum categories [PDF]
, 2009 Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set of axioms close to the definitions of a bialgebroid in the Hopf algebraic literature.
Chikhladze, Dimitri
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Derived categories of NDG categories [PDF]
Journal of Homotopy and Related Structures, 2021 We study $N$-differential graded ($NDG$) categories and their the derived categories. First, we introduce $N$-differential modules over an $NDG$ category $\mathcal{A}$. Then we show that the category $\mathsf{C}_{Ndg}(\mathcal{A})$ of $N$-differential $\mathcal{A}$-modules is a Frobenius category, and that its homotopy category $\mathsf{K}_{Ndg ...
Hiroshi Nagase, Jun-ichi Miyachi
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The dendroidal category is a test category [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2018 AbstractWe prove that the category of trees Ω is a test category in the sense of Grothendieck. This implies that the category of dendroidal sets is endowed with the structure of a model category Quillen-equivalent to spaces. We show that this model category structure, up to a change of cofibrations, can be obtained as an explicit left Bousfield ...
Ara, Dimitri +2 more
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Category Algebras and States on Categories [PDF]
Symmetry, 2021 The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras.
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The Heisenberg category of a category
, 2021 Starting with a k-linear or DG category admitting a (homotopy) Serre functor, we construct a k-linear or DG 2-category categorifying the Heisenberg algebra of the numerical K-group of the original category. We also define a 2-categorical analogue of the Fock space representation of the Heisenberg algebra.
Gyenge, Ádám +2 more
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Integral categories and calculus categories [PDF]
Mathematical Structures in Computer Science, 2018 Differential categories are now an established abstract setting for differentiation. However, not much attention has been given to the process which is inverse to differentiation: integration. This paper presents the parallel development for integration by axiomatizing an integral transformation, sA: !A → !A ⊗ A, in a symmetric monoidal category with a
Cockett, Robin, Lemay, Jean-Simon
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A model category structure on the category of simplicial categories [PDF]
Transactions of the American Mathematical Society, 2006 In this paper we put a cofibrantly generated model category structure on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence of categories.
Julia E. Bergner, Julia E. Bergner
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Subfactor Categories of Triangulated Categories [PDF]
Communications in Algebra, 2015 15 ...
Baiyu Ouyang, Panyue Zhou, Jinde Xu
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Logical Methods in Computer Science, 2019 We introduce and develop the notion of *displayed categories*. A displayed category over a category C is equivalent to "a category D and functor F : D --> C", but instead of having a single collection of "objects of D" with a map to the objects of C, the objects are given as a family indexed by objects of C,
Ahrens, Benedikt +1 more
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Australasian Journal of Plastic Surgery, 2022 Nowhere are the limitations of categorisation more apparent than in our outdated and overly simplistic surgical elective surgery categories, writes Mark Lee.
Mark Lee, Mark Ashton
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