Abstract

. We review Quillen's concept of a model category as the proper setting for defining derived functors in non-abelian settings, explain how one can transport a model structure from one category to another by mean of adjoint functors (under suitable assumptions), and define such structures for categories of cosimplicial coalgebras. 1. Introduction Model categories, first introduced by Quillen in [Q1], have proved useful in a number of areas -- most notably in his treatment of rational homotopy in [Q2], and in defining homology and other derived functors in non-abelian categories (see [Q3]; also [BoF, BlS, DwHK, DwK, DwS, Goe, ScV]). From a homotopy theorist's point of view, one interesting example of such non-abelian derived functors is the E 2 -term of the mod p unstable Adams spectral sequence of Bousfield and Kan. They identify this E 2 -term as a sort of Ext in the category CA of unstable coalgebras over the mod p Steenrod algebra (see x7.4). The original purpose of this note w...

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