Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product

Details Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product

2010-09-28

arxiv.org/abs/1009.5609v2

Mathematics

Algebraic Topology

13 pages version 2: more references and some corrections; accepted for Cah. Top. Geom. Diff. Cat

Scientific paper

The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid. The route to this corollary is through the equivalence of the category of crossed complexes with that of cubical omega-groupoids with connections where the initial definition of the tensor product lies. It is also in the latter category that we are able to apply techniques of dense subcategories to identify the tensor product of covering morphisms as a covering morphism.

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