Homotopy units in A-infinity algebras

Abstract

We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra structures on a given object is up to homotopy a subset of connected components of the space of non-unital associative algebra structures.

39 pages, the proof of the main theorem for DG-operads has been corrected, cylinders are not used any more and will be considered elsewhere

References in corpus (3)

• Homotopy theory of non-symmetric operads
• Unital associahedra
• Moduli spaces of algebras over non-symmetric operads

Cited by in corpus (5)

• Homotopy theory of non-symmetric operads II: change of base category and left properness
• Moduli spaces of algebras over non-symmetric operads
• Enhanced finite triangulated categories
• Cylinders for non-symmetric DG-operads via homological perturbation theory
• $A_{\infty }$-actions and Recognition of Relative Loop Spaces