In this paper, we study properties of maps between fibrant objects in model categories. We give a characterization of weak equivalences between fibrant objects. If every object of a model category is fibrant, then we give a simple description of a set of generating cofibrations. We show that to construct such a model structure it is enough to check some relatively simple conditions.
Keywords: Quillen model structures, fibrant objects
2010 MSC: 55U35
Theory and Applications of Categories, Vol. 33, 2018, No. 3, pp 43-66.