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A-infinity algebras, modules and functor categories

Bernhard Keller
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Abstract

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal category of cocategories. In particular, this yields a natural construction of the bialgebra structure on the bar construction of the Hochschild complex of an associative algebra.

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Bernhard Keller. 2006-02-12. A-infinity algebras, modules and functor categories. https://arxiv.org/abs/math/0510508

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