A folk Quillen model structure for operads

TL;DR

This paper constructs a new cofibrantly generated monoidal model structure on operads, enabling a better understanding of their homotopical properties and connecting to classical models of categories.

Contribution

It introduces an elementary construction of a cofibrantly generated monoidal model structure on operads, linking it to the Rezk model structure on small categories.

Findings

Established a cofibrantly generated monoidal model structure on operads

Revealed a connection to the Rezk model structure via slicing over an operad

Provided elementary methods for model structure construction

Abstract

We establish, by elementary means, the existence of a cofibrantly generated monoidal model structure on the category of operads. By slicing over a suitable operad the classical Rezk model structure on the category of small categories is recovered.