A derivability criterion based on the existence of adjunctions

Details A derivability criterion based on the existence of adjunctions A derivability criterion based on the existence of adjunctions

2012-02-15

arxiv.org/abs/1202.3359v1

Mathematics

Category Theory

14 pages

Scientific paper

In this paper we introduce a derivability criterion of functors based on the existence of adjunctions rather than on the existence of resolutions. It constitutes a converse of Quillen-Maltsiniotis derived adjunction theorem. We present two applications of our derivability criterion. On the one hand, we prove that the two notions for homotopy colimits corresponding to Grothendieck derivators and Quillen model categories are equivalent. On the other hand, we deduce that the internal hom for derived Morita theory constructed by B. To\"en is indeed the right derived functor of the internal hom of dg-categories.

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