  Combinatorial model categories were introduced by J. H. Smith as model
categories which are locally presentable and cofibrantly generated. He has not
published his results yet but proofs of some of them were presented by T. Beke
or D. Dugger. We are contributing to this endeavour by proving that weak
equivalences in a combinatorial model category form an accessible category. We
also present some new results about weak equivalences and cofibrations in
combinatorial model categories.
