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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.
Matteo Doni (Sat,) studied this question.
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