A construction of an A∞-category

A construction of an A∞-category (2002)

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by Volodymyr Lyubashenko , Sergiy Ovsienko

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@MISC{Lyubashenko02aconstruction,
    author = {Volodymyr Lyubashenko and Sergiy Ovsienko},
    title = { A construction of an A∞-category},
    year = {2002}
}

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Abstract

We construct an A∞-category D(C|B) from a given A∞-category C and its full subcategory B. The construction resembles a particular case of Drinfeld’s quotient of differential graded categories [Dri02]. We use D(C|B) to construct an A∞-functor of K-injective resolutions of a complex. The conventional derived category is obtained as the 0-th cohomology of the quotient of differential graded category of complexes over acyclic complexes.

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