Algebraic Homotopy by Hans Joachim Baues

X 1, is applied, Ob f = Kan complexes, Obc = Ob. 11) to the cofibration category of simplicial sets. 12) one obtains the next example.

4) Corollary. 10). This example shows that it is convenient to consider the class cof of cofibrations as part of the structure of an 1-category. 1). 5) Proposition. Let u:C -* D be a map in C. Suppose that C is a model category or that C is an IP-category which satisfies (M2). Then the category 4b Appendix 33 C(u) is a cofibration category with the following external structure cof =maps in C(u) which are cofibrations in C, we = maps in C(u) which are weak equivalences in C, all objects C -+X ->)D (for which z is a fibration in C) are fibrant in C(u).

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