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Article overview
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Crossed modules of rack | Alissa S. Crans
; Friedrich Wagemann
; | Date: |
17 Oct 2013 | Abstract: | We generalize the notion of a crossed module of groups to that of a crossed
module of racks. We investigate the relation to categorified racks, namely
strict 2-racks, and trunk-like objects in the category of racks, generalizing
the relation between crossed modules of groups and strict 2-groups. Then we
explore topological applications. We show that by applying the rack-space
functor, a crossed module of racks gives rise to a covering. Our main result
shows how the fundamental racks associated to links upstairs and downstairs in
a covering fit together to form a crossed module of racks. | Source: | arXiv, 1310.4705 | Services: | Forum | Review | PDF | Favorites |
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