Abstract sectional category in model structures on topological spaces

摘要

We study the behavior of the abstract sectional category in the Quillen, the Strom and the Mixed proper model structures on topological spaces and prove that, under certain reasonable conditions, all of them coincide with the classical notion. As a result, the same conclusions hold for the abstract Lusternik Schnirelmann category and the abstract topological complexity of a space. (C) 2015 Elsevier B.V. All rights reserved.