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Selecta Mathematica, 2016
We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthmüller and Grothendieck formalisms (where either $$f^{!}=f^{*}$$f!=f∗ or $$f_{!}=f_{*}$$f!=f∗) or intermediate
F. Hörmann
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REPRESENTABLE FUNCTORS, SERRE FUNCTORS, AND MUTATIONS

Mathematics of the USSR-Izvestiya, 1990
This paper studies the categorical version of the concept of mutations of an exceptional set, as used in the theory of vector bundles. The basic object of study is a triangulated category with a family of subcategories satisfying the so-called admissibility condition. A natural notion arising here is that of a Serre functor, effecting a certain duality
Alexey Bondal, M. Kapranov
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Homotopical Properties of the Simplicial Maurer–Cartan Functor

, 2016
We consider the category whose objects are filtered, or complete, L ∞ -algebras and whose morphisms are ∞-morphisms which respect the filtrations. We then discuss the homotopical properties of the Getzler–Hinich simplicial Maurer–Cartan functor which ...
Christopher L. Rogers
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mathematics
pure mathematics
algebra over a field

computer science
discrete mathematics
adjoint functors

derived functor
natural transformation
functor category