k-linear Morita theory

In this paper, we prove the standard comparison used by mathematicians between the idempotent complete pretriangulated dg-categories, over a unitary and commutative ring k, and the idempotent complete k-linear stable ∞-categories. Our approach is completely included in the ∞-categorical theory. To achieve the target we will reinterpret the Morita theory for dg-categories and we set the Morita theory for k-linear stable ∞-category.