A-infinity algebras, modules and functor categories

Details A-infinity algebras, modules and functor categories A-infinity algebras, modules and functor categories

2005-10-24

arxiv.org/abs/math/0510508v3

Mathematics

Representation Theory

errors in section 5.1 corrected, references added, 27 pages

Scientific paper

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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