A homotopy-theoretic universal property of Leinster's operad for weak omega-categories

TL;DR

This paper demonstrates that Leinster's operad for weak omega-categories serves as the universal cofibrant replacement for the operad of strict omega-categories, establishing a homotopy-theoretic universal property.

Contribution

It introduces a homotopy-theoretic universal property of Leinster's operad, linking it canonically to cofibrant replacements in weak factorization systems.

Findings

Leinster's operad is the universal cofibrant replacement for strict omega-category operad.

Provides a canonical construction of cofibrant replacements in weak factorization systems.

Connects homotopy theory with the structure of weak omega-categories.

Abstract

We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak omega-categories, showing that the universal and canonical cofibrant replacement of the operad for strict omega-categories is precisely Leinster's operad for weak omega-categories.