Holmstrom A-infinity algebra

http://mathoverflow.net/questions/57589/heuristic-behind-a-infty-algebras

See relevant nLab entries, also A-infinity space, A-infinity operad, A-infinity ring.

http://mathoverflow.net/questions/51777/is-an-a-infinity-thing-the-same-the-same-as-strict-thing-viewd-through-a-homotpy

http://mathoverflow.net/questions/51817/question-about-a-infty-maps

http://mathoverflow.net/questions/52189/higher-homotopy-algebraic-structure-on-the-homology-of-an-operad

arXiv:1205.6058 Homotopy unital A_infinity-algebras fra arXiv Front: math.AT av Volodymyr Lyubashenko It is well known that the differential graded operad of A_infinity-algebras is a cofibrant replacement (a dg-resolution) of the operad of associative differential graded algebras without units. In this article we find a cofibrant replacement of the operad of associative differential graded algebras with units. Algebras over it are called homotopy unital A_infinity-algebras. We prove that the operad bimodule of A_infinity-morphisms is a cofibrant replacement of the operad bimodule of morphisms of dg-algebras without units. Similarly we show that the operad bimodule of homotopy unital A_infinity-morphisms is a cofibrant replacement of the operad bimodule of morphisms of dg-algebras with units.

nLab page on A-infinity algebra