The cotriple resolution of differential graded algebras

TL;DR

This paper investigates the cotriple resolution in the context of differential graded algebras over operads, demonstrating that geometric realization provides a cofibrant resolution in these categories.

Contribution

It introduces a new approach to cofibrant resolutions for differential graded algebras using cotriple resolutions and geometric realization.

Findings

Cotriple resolution yields cofibrant resolutions in these categories.

Geometric realization in model categories is effective for these resolutions.

Applicable to algebras over the Barratt-Eccles operad and commutative algebras.

Abstract

We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded Barratt-Eccles operad and on the example of commutative alegbras. We prove that the geometric realization of the cotriple resolution (in the sense of model categories) gives a cofibrant resolution functor on these categories of differential graded algebras.