Closed multicategories and $A_\infty$-categories

Abstract:
We have constructed closed multicategory of $A_\infty$-categories. For this purpose we develop the theory of enriched and closed multicategories, investigate general and some special multimonads, construction of Kleisli, Kleisli multicategory of graded quivers, discover the free category Hopf monad, etc. Possible applications to homological algebra are discussed.