Homotopy unital A_infinity-algebras
K-Theory and Homology
2012-05-29 v1 Algebraic Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1205.6058,
title = {Homotopy unital A_infinity-algebras},
author = {Volodymyr Lyubashenko},
journal= {arXiv preprint arXiv:1205.6058},
year = {2012}
}
Comments
26 pages