Homotopy coherent representations

TL;DR

This paper discusses the concept of homotopy coherence in representations, providing a historical overview and clarifying its significance in the context of symmetries and strong homotopy representations.

Contribution

It offers a semi-historical survey of homotopy coherence in representations, highlighting its development and connections to related concepts.

Findings

Historical links and terminology clarified

Homotopy coherence's role in symmetry analysis explained

Connections to strong homotopy representations discussed

Abstract

Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is: Homotopy coherence of representations, at one time known as strong homotopy representations. We provide a brief semi-historical survey providing some links that may not be common knowledge.