Abstract
We rethink the notion of derived functor in terms of corre-spondences, that is, functors ε → [1]. While derived functors in our sense, when they exist, are given by Kan extensions, their existence is a strictly stronger property than the existence of Kan extensions. We show, however, that derived functors exist in the cases one expects them to exist. Our definition is espe-cially 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 such a passage is immediate in our approach. Our approach makes perfect sense in the context of ∞-categories.
Original language | English |
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Pages (from-to) | 279-293 |
Number of pages | 15 |
Journal | Homology, Homotopy and Applications |
Volume | 22 |
Issue number | 2 |
DOIs | |
State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020, Vladimir Hinich.
Keywords
- Derived functor
- ∞-category
ASJC Scopus subject areas
- Mathematics (miscellaneous)