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

Ronald Brown, Ross Street

    Research output: Contribution to journalArticlepeer-review

    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 languageEnglish
    Pages (from-to)188-208
    Number of pages21
    JournalCahiers de topologie et géométrie différentielle catégoriques
    Volume52
    Issue number3
    Publication statusPublished - 2011

    Keywords

    • crossed complexes
    • cubical omega-groupoids
    • monoidal closed
    • density
    • covering morphisms

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