English

Quotients of unital ${A}_\infty$-categories

Category Theory 2008-02-17 v5 K-Theory and Homology

Abstract

For a full subcategory B of a unital A_infinity-category C a quotient unital A_infinity-category `C/B' is defined. For differential graded categories such quotient is constructed by V.Drinfeld. Our construction is explicit and uses freely generated A_infinity-categories. The quotient D=`C/B' represents the A_infinity-2-functor A \mapsto A_\infty^u(C,A)_{modulo B}, which associates with a given unital A_infinity-category A the A_infinity-category of unital A_infinity-functors C -> A, whose restriction to B is contractible.

Keywords

Cite

@article{arxiv.math/0306018,
  title  = {Quotients of unital ${A}_\infty$-categories},
  author = {Volodymyr Lyubashenko and Oleksandr Manzyuk},
  journal= {arXiv preprint arXiv:math/0306018},
  year   = {2008}
}

Comments

92 pages, LaTeX, uses Paul Taylor's diagrams.sty; the A_infiniti Yoneda Lemma is referred to another paper instead of being proved. Resubmitted for TeXnical reasons