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Semisimplicial objects and the Eilenberg-Zilber theorem

✍ Scribed by D. B. A. Epstein


Publisher
Springer-Verlag
Year
1966
Tongue
English
Weight
474 KB
Volume
1
Category
Article
ISSN
0020-9910

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We give a natural strong deformation retraction from the fundamental homotopy crossed complex of a product of simplicial sets onto the tensor product of the corresponding crossed complexes. This generalises the classical theorem of Eilenberg and Zilber to a non-abelian setting. Explicit crossed comp

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We state the Eilenberg-Zilber type theorem for the product of two small categories and consider the Bredon homology of an equivariant space with local coefficients in the light of homologies of small categories. Then, in particular, an exterior product, Künneth formula and cap-product for the Bredon