Corrections to "Homotopy theory of nonsymmetric operads, I, II"

TL;DR

This paper corrects a mistake in the construction of push-outs in the homotopy theory of nonsymmetric operads, ensuring the accuracy of previous results in the field.

Contribution

It provides necessary corrections to prior foundational work on nonsymmetric operads, fixing errors in the construction of push-outs and related results.

Findings

Corrected the construction of push-outs along free morphisms

Fixed affected results in previous papers

Ensured the validity of the homotopy theory framework for nonsymmetric operads

Abstract

We correct a mistake in the construction of push-outs along free morphisms of algebras over a nonsymmetric operad in arXiv:1101.1634 [math.AT], and we fix the affected results in arXiv:1101.1634 [math.AT] and arXiv:1304.6641 [math.AT].