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

By Kamps K.H., Porter T.

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PORTER and might be called a 3-cocycle condition. ) We are, however, approaching the limits of what is known at this point, so need to look where we are. There are several important remarks to make and questions to ask: 1. Is the problem of finding a structure for c(CG ) reasonably posed, at the right level of generality? In attempting to get around the non-composability of the (H, f ), we have considered pairs (g1 , g2 ) of composable arrows in G. That is reminiscent of constructions within the nerve of G and, of course, the diagram for the 3-cocycle condition came from a 3-simplex in that nerve.

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And Kieboom, R. : A homotopy 2-groupoid of a Hausdorff space, Appl. Categ. Structures 8 (2000), 209–234. 2-GROUPOID ENRICHMENTS IN HOMOTOPY THEORY 409 [JS] Joyal, A. : Braided tensor categories, Adv. Math. 102 (1993), 20–78. [JT] Joyal, A. : Algebraic homotopy types (in preparation). [Ka] Kamps, K. : Note on normal sequences of chain complexes, Colloq. Math. 39 (1978), 225–227. [KP] Kamps, K. : Abstract Homotopy and Simple Homotopy Theory, World Scientific, Singapore, 1997. [Ke] Kelly, G. : The Basic Concepts of Enriched Category Theory, London Math.

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