By Kamps K.H., Porter T.

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Extra info for 2-Groupoid Enrichments in Homotopy Theory and Algebra

Example text

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. Algebra 34 (1984), 155–178. : Sur la notion de diagramme homotopiquement coh´erent, 3`eme Colloque sur les Cat´egories, Amiens, 1980, Cahiers Top.

If (C, ⊗, I ) is a braided monoidal category, with C small, then a representation of C will be a (G2 , ⊗)-functor from C to another (G2 , ⊗)-category D, say. The question is: what is the categorical structure of the class of all representations of C in D. e. g. a (G2 , ⊗)-enrichment that can be usefully derived? ) A second potential application is within Grothendieck’s Pursuing Stacks [Gro]. That programme requires the study of actions of n-types on (n − 1)-types. A 3-type is representable by a (G2 , ⊗)-groupoid as we have noted and the category of 2types ‘is’ the ‘category’ of 2-groupoids.

Modules crois´es g´en´eralis´es de longueur 2, J. Pure Appl. Algebra 34 (1984), 155–178. : Sur la notion de diagramme homotopiquement coh´erent, 3`eme Colloque sur les Cat´egories, Amiens, 1980, Cahiers Top. G´eom. Diff. 23 (1982), 93–112. -M. : Vogt’s theorem on categories of coherent diagrams, Math. Proc. Cambridge Philos. Soc. 100 (1986), 65–90. Crans, S. : A tensor product for Gray-categories, Theory Appl. Categ. 5 (1999), 12– 69. : Cat´egories structur´ees III: Quintettes et applications covariantes, Cahiers Topologie G´eom.

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