Subject: model categories Date: Mon, 21 Apr 2003 22:56:54 -0400 (EDT) From: Tom Goodwillie To: dmd1@lehigh.edu (Don Davis) > > Subject: about cofibrant objects > Date: Mon, 21 Apr 2003 15:18:20 +0200 (MEST) > From: Philippe Gaucher > > Hello [question for the mailing list] > > I would be interested in knowing examples of model categories whose > terminal object is not cofibrant. > > Thanks in advance. pg. If C is a model category and f:A->B is a morphism of C then consider the category of "objects between A and B": Objects are factorizations A->X->B of f, and maps (A->X->B)->(A->Y->B) are commutative diagrams A -> X -> B 1 | | | 1 V V V A -> Y -> B This is a model category, with cofibrations (resp. fibrations resp. weak equivalences) being maps such that the underlying map in C is a cofibration (resp. fib resp. wk eq). If f is not a cofibration in C, then the final object in this new category is not cofibrant. - Tom Goodwillie