Homotopic Chain Maps Have Equal s-Homology and d-Homology

Homotopic Chain Maps Have Equal s-Homology and d-Homology

The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established. As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractibl...

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Veröffentlicht in:International Journal of Mathematics and Mathematical Sciences 2016, Vol.2016 (2016), p.158-162
1. Verfasser: M. Z. Kazemi-Baneh
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Categories
Chains
Homology
Homology theory (Mathematics)
Homotopy theory
Mappings (Mathematics)
Mathematical analysis
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Zusammenfassung:The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and d-homologies of homotopic chain maps is established. As a special case, if X and Y are the same homotopy type, then their nth d-homology R-modules are isomorphic, and if X is a contractible space, then its nth d-homology R-modules for n≠0 are trivial.
ISSN:0161-1712
1687-0425
DOI:10.1155/2016/5647548