We define natural A∞-transformations and construct А∞-category of ∞-functors. The notion of strict units in an A∞ category is made weaker. The 2-category o] A∞-categories, functors and transformations is described. We study quotient of an A∞-category over a full subcategory. The conventional derived category is obtained as the 0-th cohomology of the quotient of differential graded category of complexes over acyclic
complexes.