Corrections to the article: Operadic definition of the non-strict cells

TL;DR

This paper introduces a new concept of contractibility for coloured ω-operads and offers an alternative method to construct the monad for free contractible coloured ω-operads, enhancing the theoretical framework.

Contribution

It presents a novel notion of contractibility and a new approach to building the monad for free contractible coloured ω-operads, advancing operadic theory.

Findings

New notion of contractibility for coloured ω-operads

Alternative construction method for the monad

Enhanced theoretical understanding of operadic structures

Abstract

In this short notes we propose a new notion of contractibility for coloured $\omega$-operad defined in the article published in Cahiers de Topologie et de G{\'e}om{\'e}trie Diff{\'e}rentielle Cat{\'e}gorique (2011), volume 4. We propose also an other way to build the monad for free contractible coloured $\omega$-operads.