Abstract

GAITAN-OSPINA, RAFAEL. Homoto-Homological Skeleton in the Category of Abelian Groups. Integración - UIS [online]. 2021, vol.39, n.2, pp.137-176.  Epub Apr 18, 2022. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n2-2021002.

In this paper, we present the construction of a general homology theory in the category of abelian groups in the sense of the textbook Introducción a la Teoría de Homología General by R. Ruiz [22], to general categories, meeting axioms similar to those presented by Eilenberg and Steenrod in homology theories for admissible categories of topological pairs (X, A) [3]. We built this general homology theory in abelian groups through what we called Homoto-Homological Skeleton, showing the connections with monoidal categories and simplicial categories.

Keywords : Simplicial sets; simplicial abelian groups; homotopy; homology; homotopic system; singular functor; admissible categories; model object.

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