Results 1 to 10 of about 1,060 (227)
The Uniform Homotopy Category [PDF]
Journal of Pure and Applied Algebra, 2021 This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the respective Lipschitz and uniform settings.
Sanjeevi Krishnan, Crichton Ogle
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Entropy, 2023 Universal Causality is a mathematical framework based on higher-order category theory, which generalizes previous approaches based on directed graphs and regular categories.
Sridhar Mahadevan
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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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Homotopy cartesian squares in extriangulated categories
Open Mathematics, 2023 Let (C,E,s)\left({\mathcal{C}},{\mathbb{E}},{\mathfrak{s}}) be an extriangulated category. Given a composition of two commutative squares in C{\mathcal{C}}, if two commutative squares are homotopy cartesian, then their composition is also a homotopy ...
He Jing, Xie Chenbei, Zhou Panyue
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Relative global dimensions and stable homotopy categories [PDF]
Comptes Rendus. Mathématique, 2020 In this paper we study the finiteness of global Gorenstein AC-homological dimensions for rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an application, we show that any left (or right) coherent and left Gorenstein ring
Liang, Li, Wang, Junpeng
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Generalized Homotopy in C- Categories [PDF]
, 2001 A \(C\)-category is a category with a class of fibrations and a cone endofunctor \(C\) subject to suitable axioms. The authors define homotopy groups associated to pairs of morphisms of the form \(i: B\to A\), \(h: CA\to X\) in a \(C\)-category, where \(i\) is a cofibration.
Sergio Rodríguez Machín +2 more
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Homotopy Category of Cotorsion Flat Representations of Quivers [PDF]
Mathematics Interdisciplinary Research, 2020 Recently in [10], it was proved that over any ring R, there exists a complete cotorsion pair (Kp(Flat-R); K(dg-CotF-R)) in K(Flat-R), the homotopy category of complexes of flat R-modules, where Kp(Flat-R) and K(dg-CotF-R) are the homotopy categories ...
Hossein Eshraghi
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Homotopies of 2-Algebra Morphisms
Communications in Advanced Mathematical Sciences, 2022 In [1] it is defined the notion of 2-algebra as a categorification of algebras, and shown that the category of strict 2-algebras is equivalent to the category of crossed modules in commutative algebras.
Ummahan Ege Arslan, İbrahim Akça
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Lie algebras with differential operators of any weights
Electronic Research Archive, 2023 In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight.
Yizheng Li, Dingguo Wang
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Combinatorial Homotopy Categories [PDF]
, 2020 A model category is called combinatorial if it is cofibrantly generated and its underlying category is locally presentable. As shown in recent years, homotopy categories of combinatorial model categories share useful properties, such as being well generated and satisfying a very general form of Ohkawa's theorem.
Casacuberta, Carles, Rosicky, Jiri
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