Quotients of unital A∞-categories
Volodymyr Lyubashenko, Oleksandr Manzyuk
Abstract
For a full subcategory B of a unital Ainfinity-category C a quotient unital Ainfinity-category `C/B' is defined. For differential graded categories such quotient is constructed by V.Drinfeld. Our construction is explicit and uses freely generated Ainfinity-categories. The quotient D=`C/B' represents the Ainfinity-2-functor A A∞u(C,A)modulo B, which associates with a given unital Ainfinity-category A the Ainfinity-category of unital Ainfinity-functors C -> A, whose restriction to B is contractible.
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