What do abelian categories form?

Abstract

This is mostly an overview. Given finitely presentable abelian categories $A$ and $B$, we sketch the construction of an abelian category of continuous functors from $A$ to $B$ that has nice $2$-categorical behaviour and gives an explicit model for the stable category of stable functors between the derived categories of $A$ and $B$. The construction is absolute, thus allows one to recover not only Hochschild but also Mac Lane Cohomology.

56 pages, LaTeX2e. Relatively minor changes: improved the exposition, fixed some mistakes (all the results are either unaffected or actually strengthened)

References in corpus (1)

• Adjunction in 2-categories