So, what is a derived functor?

Abstract

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair (LF,RG). In particular, canonicity of this passage becomes obvious. 2nd version: added comparison to Deligne's definition (SGA4) and a discussion of diagrams of derived functors. Introduction rewritten and references added. 3rd version: description of Kan extensions in terms of correspondences more detailed. 4th version: the final version accepted to HHA.

12 pages, Version 3: 16 pages

References in corpus (4)

• Higher Topos Theory
• Yoneda lemma for enriched infinity categories
• Lectures on infinity categories
• Descent Theory and Mapping Spaces

Cited by in corpus (1)

• Parametrized spectra, a low-tech approach