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Topological data analysis and topological deep learning beyond persistent homology: a review. [PDF]
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Applied Categorical Structures, 2008
From the reviewer's point of view, the main notion of the paper (``abelian grouped category'', in Section 1.2) should be made precise. In order to consider condition (ii), the abelian group structure every object is assumed to have by (i), has to be part of the structure. Moreover, the notion ``set function'' appearing in Section 1.3 is not defined.
Bian, Ning, Zhang, Pu, Zhang, Guang-Lian
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From the reviewer's point of view, the main notion of the paper (``abelian grouped category'', in Section 1.2) should be made precise. In order to consider condition (ii), the abelian group structure every object is assumed to have by (i), has to be part of the structure. Moreover, the notion ``set function'' appearing in Section 1.3 is not defined.
Bian, Ning, Zhang, Pu, Zhang, Guang-Lian
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On a Strange Homotopy Category
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Explicit Ladder of Homotopy Categories
Chinese Annals of Mathematics, Series B, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Groupoid Enriched Categories and Homotopy Theory
Canadian Journal of Mathematics, 1983We are concerned in this paper with category-theoretic aspects of homotopy theory. Originally, category theory developed as a simplifying language in the context of algebraic topology and yet one primary example: the category Π of spaces and homotopy classes of maps admits only limited use of the language owing to the very sparse occurrence of limits ...
Fantham, P. H. H., Moore, E. J.
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The Homotopy category of homotopy factorizations
1987K. A. Hardie, K. H. Kamps
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The homotopy category of acyclic complexes of pure-projective modules
Forum Mathematicum, 2023exaly
Digital H-spaces and actions in the pointed digital homotopy category
Applicable Algebra in Engineering, Communications and Computing, 2019Dae-Woong Lee
exaly