Flasque model structures for simplicial presheaves. (English summary) K-Theory 36 (2005), no. 3-4, 371–395 (2006).1573-0514 The categories of simplicial presheaves have been found to be central to many areas of algebraic topology, algebraic geometry and category theory. In particular, the various contending useful homotopy structures on it have been the source of much study as none of them so far studied is without its problems. Typically there is a good class of cofibrations, or of fibrations, but the orthogonal class of fibrations, resp. cofibrations, is much less easy to handle or to gain any intuition of its geometric meaning. The author proposes here a very neat alternative to the more usual projective and injective structures. This ‘flasque ’ model structure uses classes of cofibrations and fibrations that are both manageable, but, of course, are not as simply defined as the corresponding injective or projective ones. Comparisons with other possible or related solutions of this problem are given
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