From: Michael Batanin <mbatanin@mpce.mq.edu.au>
To: categories@mta.ca
Subject: Re: strictification
Date: Thu, 07 Jan 1999 09:56:57 +1100 [thread overview]
Message-ID: <3693EA39.139F@mpce.mq.edu.au> (raw)
In-Reply-To: <Pine.SOL.3.96.990106062756.29331G-100000@cupid.math.unc.edu>
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
>
> http://www.math.unc.edu/Faculty/jds
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.
next prev parent reply other threads:[~1999-01-06 22:56 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
1999-01-06 11:28 strictification James Stasheff
1999-01-06 22:56 ` Michael Batanin [this message]
1999-01-07 7:49 strictification Carlos Simpson
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