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.