English

What do abelian categories form?

Category Theory 2022-05-18 v2 Algebraic Geometry

Abstract

This is mostly an overview. Given finitely presentable abelian categories AA and BB, we sketch the construction of an abelian category of continuous functors from AA to BB that has nice 22-categorical behaviour and gives an explicit model for the stable category of stable functors between the derived categories of AA and BB. The construction is absolute, thus allows one to recover not only Hochschild but also Mac Lane Cohomology.

Keywords

Cite

@article{arxiv.2112.02155,
  title  = {What do abelian categories form?},
  author = {D. Kaledin},
  journal= {arXiv preprint arXiv:2112.02155},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-24T08:03:45.435Z