Every Q-shaped derived category, under mild assumptions, is equivalent to the derived category of differential graded bimodules over a dg category built from the shape Q.
Une structure de cat´ egorie de mod` eles de Quillen sur la cat´ egorie des dg-cat´ egories
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$Q$-shaped derived categories as derived categories of differential graded bimodules
Every Q-shaped derived category, under mild assumptions, is equivalent to the derived category of differential graded bimodules over a dg category built from the shape Q.