2014/07/07 by Ilan Barnea, Barnea, Ilan, Tomer M. Schlank +1
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1407.1817
openalex publication_date 2014/07/07 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In a recent paper we introduced a much weaker and easy to verify structure\nthan a model category, which we called a "weak fibration category". We further\nshowed that a small weak fibration category can be "completed" into a full\nmodel category structure on its pro-category, provided the pro-category\nsatisfies a certain two out of three property. In the present paper we give\nsufficient intrinsic conditions on a weak fibration category for this two out\nof three property to hold. We apply these results to prove theorems giving\nsufficient conditions for the finite accessibility of the category of weak\nequivalences in combinatorial model categories. We apply these theorems to the\nstandard model structure on the category of simplicial sets, and deduce that\nits class of weak equivalences is finitely accessible. The same result on\nsimplicial sets was recently proved also by Raptis and Rosick 'y, using\ndifferent methods.\n