We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak equivalences between simplicial sets is finitely accessible.
Keywords: model category, weak equivalence, accessible category
2010 MSC: 55U35, 18C35
Theory and Applications of Categories, Vol. 30, 2015, No. 19, pp 687-703.