Homotopy unital A_infinity-algebras

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.

26 pages

References in corpus (1)

• Unital $A_{\infty }$-categories

Cited by in corpus (8)

• Unital associahedra
• Enhanced $A$-infinity obstruction theory
• Diagonals and A-infinity Tensor Products
• Dihedral and reflexive modules with $\infty$-simplicial faces and dihedral and reflexive homology of involutive $A_{\infty }$-algebras over unital commutative rings
• Curved Koszul duality of algebras over unital versions of binary operads
• Strictly unital A-infinity algebras
• Cylinders for non-symmetric DG-operads via homological perturbation theory
• A_infinity-morphisms with several entries