Results 11 to 20 of about 31,935 (188)
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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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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Homotopy invariants of singularity categories [PDF]
Journal of Pure and Applied Algebra, 2020 final ...
Gratz, Sira, Stevenson, Greg
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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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A uniqueness theorem for stable homotopy theory [PDF]
, 1999 In this paper we study the global structure of the stable homotopy theory of spectra. We establish criteria for when the homotopy theory associated to a given stable model category agrees with the classical stable homotopy theory of spectra.
Schwede, Stefan, Shipley, Brooke
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Simplicial presheaves of coalgebras [PDF]
, 2011 The category of simplicial R-coalgebras over a presheaf of commutative unital rings on a small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated model category structure where the weak equivalences are the local weak ...
Brown +11 more
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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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Fredholm modules over categories, Connes periodicity and classes in cyclic cohomology
Comptes Rendus. Mathématique, 2023 We replace a ring with a small $\mathbb{C}$-linear category $\mathcal{C}$, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the cyclic ...
Balodi, Mamta, Banerjee, Abhishek
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