Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product | Macquarie University ResearchOnline

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Title: Covering morphisms of crossed complexes and of cubical omega-groupoids are closed under tensor product
Related: Cahiers de topologie et géométrie différentielle catégoriques, Vol. 52, No. 3, (2011), p.188-208
Publisher: Cahiers de Topologie et Geometrie Differentielle Categoriques
Date: 2011
Author/Creator: Brown, Ronald
Author/Creator: Street, Ross
Description: The aim is the proof of 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 w-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.
Description: 21 page(s)
Subject Keyword: crossed complexes
Subject Keyword: cubical omega-groupoids
Subject Keyword: monoidal closed
Subject Keyword: density
Subject Keyword: covering morphisms
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

Macquarie University ResearchOnline