Geodesic
So, what is a derived functor?
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 279-293.

Voir la notice de l'article provenant de la source International Press of Boston

We rethink the notion of derived functor in terms of correspondences, that is, functors $\mathcal{E} \to [1]$. 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 especially convenient for the description of a passage from an adjoint pair $(F,G)$ of functors to a derived adjoint pair $(\mathbf{L}F, \mathbf{R}G)$. In particular, canonicity of such a passage is immediate in our approach. Our approach makes perfect sense in the context of $\infty$-categories.
DOI : 10.4310/HHA.2020.v22.n2.a18
Classification : 18G10, 18G55
Keywords: derived functor, $\infty$-category 
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     author = {Vladimir Hinich},
     title = {So, what is a derived functor?},
     journal = {Homology, homotopy, and applications},
     pages = {279--293},
     publisher = {mathdoc},
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     number = {2},
     year = {2020},
     doi = {10.4310/HHA.2020.v22.n2.a18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a18/}
}
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Vladimir Hinich. So, what is a derived functor?. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 279-293. doi : 10.4310/HHA.2020.v22.n2.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a18/

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