A-INFINITY ALGEBRAS, MODULES AND FUNCTOR CATEGORIES
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.~Lefèvre'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.
Bernhard Keller, le 28 octobre 2005.