Algebraic Topology: Lecture 6
We completed the proof that the localization of a model category
C with respect to the class of weak equivalences exists. Recall
that this means that there exists a functor F : C --> Ho(C) with
the following properties: (i) If f is a weak equivalence in C
then F(f) is an isomorphism in Ho(C). (ii) If G : C --> D is a
functor such that G(f) is an isomorphism in D whenever f is a
weak equivalence in C, then there exists a unique functor
H : Ho(C) --> D such that G = H o F. For reading see
Paragraph 1 of Chapter 1 of Quillen's paper.