James Stasheff wrote:
Is there a strictification result for A_infty-cats? If so, under what hypotheses? and by whome? where?
.oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250
Yes. Im my paper "Homotopy coherent category theory and A_{\infty}-structures in monoidal categories" JPAA, 123 (1988), 67-103, theorems 2.3, 2.4 and corollary 2.3.1.. In this paper I define A_{\infty}-categories as algebras in the category of K-graphs over A_{\infty}-K-operads, where K is a simplicial monoidal category with Quillen model structure such that tensor commutes with simplicial realization functor. I show that every locally fibrant A_{\infty}-category (i.e. Hom(a,b) is fibrant object in K for every a and b) is equivalent in some homotopy coherent sense to a honest K-category. Michael Batanin.