Subject: question
From: "Gennady Kondratiev"
Date: Wed, 22 Nov 2006 18:18:17 +0000
May I ask a question? 2-equivalent categories (let them be topological
subcategories) should be homotopically the same, i.e. have the same
homotopical invariants. But they are not, e.g. H^*(G) is not isomorphic to
H^*(BG), where B is classifying space functor.
Maybe, somebody knows what should at least hold for (some) homotopy
invariants of 2-equivalent (topological) categories A and B. E.g., is
there any duality like Eilenberg-Moore spectral sequence
H^*(X)\tensor H^*(FX) --> 0, where F: A --> B is a 2-equivalence? Or,
there are no relations between homotopy invariants?
Thank you!
Gennadii.