Calculating maps between n-categories
Carlos Simpson
Abstract
We give an explicit way of calculating the set of homotopy classes of morphisms from a Tamsamani n-category A to another one B. This calculation uses a Reedy-cofibrant cosimplicial resolution of A, using a new notion of ``free cofibration'' of n-precats. The free cofibrations of n-precats seem to be the analogue for n-categories of the Bousfield-Kan cofibrations in the theory of diagrams.
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