Results 11 to 20 of about 1,060 (227)
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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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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Homotopy invariants of singularity categories [PDF]
Journal of Pure and Applied Algebra, 2020 final ...
Gratz, Sira, Stevenson, Greg
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Adjointness of Suspension and Shape Path Functors [PDF]
Mathematics Interdisciplinary Research, 2021 In this paper, we introduce a subcategory ∼Sh* of Sh* and obtain some results in this subcategory. First we show that there is a natural bijection Sh(∑(X, x), (Y,y))≅Sh((X,x),Sh((I, Ī),(Y,y))), for every (Y,y)∈ ~Sh* and (X,x)∈ Sh*. By this fact, we prove
Tayyebe Nasri +2 more
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Digital homotopic distance between digital functions
Applied General Topology, 2021 In this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as being digitally homotopy invariance.
Ayse Borat
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A homotopy category for graphs [PDF]
Journal of Algebraic Combinatorics, 2020 We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call `spider moves'. We then create a category by modding out by the 2-cells of our 2-category, and use the spider moves to show that for finite graphs, this ...
Tien Chih, Laura Scull
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A Model of Directed Graph Cofiber
Axioms, 2022 In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms.
Zachary McGuirk, Byungdo Park
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Path homology theory of edge-colored graphs
Open Mathematics, 2021 In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau.
Muranov Yuri V., Szczepkowska Anna
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The homotopy category of chain complexes is a homotopy category [PDF]
Colloquium Mathematicum, 1982 Using the reviewer's characterization of fibrations and cofibrations of chain complexes [ibid. 39, 225-227 (1978; Zbl 0403.55001)] the authors show that the category of chain complexes over an Abelian category with chain homotopy equivalences as weak equivalences is a closed model category in the sense of \textit{D. G.
Golasiński, Marek, Gromadzki, Grzegorz
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