Cylinders for non-symmetric DG-operads via homological perturbation theory

Abstract

We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity operad, yields the operad parametrizing A-infinity maps whose linear part is the identity. We also compute some other examples with non-trivial operations in arities 1 and 0.

33 pages

References in corpus (3)

• Sur les A-infini catégories
• Homotopy theory of non-symmetric operads
• Homotopy unital A_infinity-algebras

Cited by in corpus (1)

• Enhanced $A$-infinity obstruction theory