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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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Recursion Operators and Frobenius Manifolds [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 In this note I exhibit a ''discrete homotopy'' which joins the category of F-manifolds to the category of Poisson-Nijenhuis manifolds, passing through the category of Frobenius manifolds.
Franco Magri
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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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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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Modalities in homotopy type theory [PDF]
Logical Methods in Computer Science, 2020 Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes.
Egbert Rijke +2 more
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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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Comparison theorems for Kan, faintly universal and strongly universal derived functors [PDF]
Surveys in Mathematics and its Applications, 2022 We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature.
Alisa Govzmann +2 more
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On some p-differential graded link homologies
Forum of Mathematics, Pi, 2022 We show that the triply graded Khovanov–Rozansky homology of knots and links over a field of positive odd characteristic p descends to an invariant in the homotopy category finite-dimensional p-complexes.
You Qi, Joshua Sussan
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