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

Ronald Brown; Ross Street

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

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Abstract

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.

Original language	English
Pages (from-to)	188-208
Number of pages	21
Journal	Cahiers de topologie et géométrie différentielle catégoriques
Volume	52
Issue number	3
Publication status	Published - 2011

Keywords

crossed complexes
cubical omega-groupoids
monoidal closed
density
covering morphisms

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abstract = "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.",

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author = "Ronald Brown and Ross Street",

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AU - Brown, Ronald

AU - Street, Ross

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N2 - 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.

AB - 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.

KW - crossed complexes

KW - cubical omega-groupoids

KW - monoidal closed

KW - density

KW - covering morphisms

M3 - Article

VL - 52

SP - 188

EP - 208

JO - Cahiers de topologie et géométrie différentielle catégoriques

JF - Cahiers de topologie et géométrie différentielle catégoriques

SN - 1245-530X

IS - 3

ER -