Model structures on the category of ex-spaces (Q1602959)

The homotopy theory of ex-spaces, exposed by James for example, is developed in the paper under review using the Quillen model category. This language is considered by the authors to be closest to a standard language for modern homotopy theory. The paper is divided in three main parts. The first part gives a brief synopsis of \textit{L. G. Lewis}'s work [ibid. 19, 75-89 (1985; Zbl 0559.18005)], several examples and a minimum of model category technicalities. The generalizations to the equivariant setting are given in the second part. The last part contains the necessary facts on (topological) model categories. The paper addresses a broad audience, avoiding high technical results, especially in the first two parts. Those familiar with model categories will find the last two sections of interest concerning the notion of intersection model structures and some other general approaches.