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

摘要

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