Quotients of unital $A_{\mathrm{\infty }}$-categories

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.