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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. Diff´erentielle Categ. 5 (1963), 1–22. Eilenberg, S. and Kelly, G. : Closed categories, In: Proc. Conference on Categorical Algebra, (La Jolla, 1965), Springer, New York, 1966, pp.

Spaces with finitely many non-trivial homotopy groups, J. Pure Appl. Algebra 24 (1982), 179–202. : Homology, Springer, Berlin, 1967. : Approche en dimension sup´erieure des 3-cat´egories augment´ees d’Olivier Leroy, Th`ese, Univ. Montpellier II, 1999. [MP] Mutlu, A. : Iterated Peiffer pairings in the Moore complex of a simplicial group, Appl. Categ. Struct. 9 (2001), 111–130. : Abstract homotopy theory: the interaction of category theory and homotopy theory, Preprint, 2001. : Homotopy types of strict 3-groupoids, e-print math.

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. by passing to the homotopy category but at level 2.

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

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