Geodesic
A construction of quotient $A_{\infty}$-categories
Homology, homotopy, and applications, Tome 8 (2006) no. 2, pp. 157-203.

Voir la notice de l'article provenant de la source International Press of Boston

We construct an $A_\infty$-category ${\mathsf D}({\mathcal C}|{\mathcal B})$ from a given $A_\infty$-category ${\mathcal C}$ and its full subcategory ${\mathcal B}$. The construction is similar to a particular case of Drinfeld's construction of the quotient of differential graded categories. We use ${\mathsf D}({\mathcal C}|{\mathcal B})$ to construct an $A_\infty$-functor of K-injective resolutions of a complex, when the ground ring is a field. The conventional derived category is obtained as the 0-th cohomology of the quotient of the differential graded category of complexes over acyclic complexes. This result follows also from Drinfeld's theory of quotients of differential graded categories.
DOI : 10.4310/HHA.2006.v8.n2.a9
Classification : 16E45, 18G10, 18G55, 57T30
Keywords: $A_{\infty}$-category, $A_{\infty}$-functor, $A_{\infty}$-transformation, $K$-injective resolution, quotient $A_{\infty}$-category 
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     title = {A construction of quotient $A_{\infty}$-categories},
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     pages = {157--203},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n2.a9/}
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Volodymyr Lyubashenko; Sergiy Ovisienko. A construction of quotient $A_{\infty}$-categories. Homology, homotopy, and applications, Tome 8 (2006) no. 2, pp. 157-203. doi : 10.4310/HHA.2006.v8.n2.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2006.v8.n2.a9/

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