A homotopy-theoretic universal property of Leinster's operad for 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.

14 pages; v2: final journal version

Cited by in corpus (3)

• Algebraic weak factorisation systems I: accessible AWFS
• The Frobenius Condition, Right Properness, and Uniform Fibrations
• $\omega$-weak equivalences between weak $\omega$-categories