Subject: about rectification of homotopy commutative diagram
From: Gaucher Philippe
Date: Fri, 8 Jun 2007 12:18:17 +0200
Dear all,
Consider the small category I: 0->1->2->... Let M be a model category
(good
enough, proper, etc...). A morphism of M^I looks like a ladder, i.e. a
diagram over another small category L(I) having the shape of a ladder. I
know
how to rectify a homotopy commutative diagram of Ho(M)^L(I), that is how
to
construct an object of Ho(M^L(I)) sent by the map Ho(M^L(I))->Ho(M)^L(I)
to
the morphism of M^I we are considering. Is it realistic to think that the
same result holds if I is any direct Reedy category ?
Thanks in advance. pg.