By Kamps K.H., Porter T.

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Morphisms. In our situation it is relatively easy to compose the 1-arrows (α, H, f ) but it only makes sense up to homotopy as there has to be a choice made between two ‘obvious’ ways to do it. c. c. e. ), see [Ba], and the fact that the situation in ω-Cat is richer, ([Cr], Section 9 again). Several of our examples of (G2 , ⊗)-categories also have a ω-Cat structure and in fact as we remarked, the (G2 , ⊗)-structure we have given is the truncation of that ω-Cat structure (most notably for Ch). e.

Categorical structures, In: Handbook of Algebra, Vol. 1, Elsevier, Amsterdam, 1996, pp. 529–577. : The role of Batanin’s monoidal globular categories, In: E. Getzler et al. (eds), Higher Category Theory. Workshop on Higher Category Theory and Physics (Evanston, 1997), Contemp. Math. 230, Amer. Math. , Providence, 1998, pp. 99–116. [V] Vogt, R. : Homotopy limits and colimits, Math. Z. 134 (1973), 11–52.

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. 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.