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By Kamps K.H., Porter T.

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4. Conclusion We have tried to indicate some of the ways in which (G2 , ⊗)-categories arise in algebra and topology, both as large examples such as Top and Ch and small ones modelling homotopy 3-types or as braided monoidal categories that might arise as categories of representations. We have seen how ‘over’ and ‘under’ categories can be constructed with homotopy coherent versions, but that the ‘homotopy coherent’ versions of categories of G-objects in a (G2 , ⊗)-category hit problems that are not resolved as yet.

A homotopy double groupoid of a Hausdorff space, Theory Appl. Categ. 10 (2002) 71–93. Brown, R. : Crossed complexes and non-Abelian extensions, In: Category Theory, Applications to Algebra, Logic and Topology, Proceedings, Gummersbach, 1981, Lecture Notes in Math. 962, Springer, Berlin, 1982, pp. 39–50. Brown, R. and Mosa, G. : Double categories, 2-categories, thin structures and connections, Theory Appl. Categ. 5 (1999), 163–175. : Modules crois´es g´en´eralis´es de longueur 2, J. Pure Appl.

Homotopy limits and colimits, Math. Z. 134 (1973), 11–52.

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2-Groupoid Enrichments in Homotopy Theory and Algebra by Kamps K.H., Porter T.


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