Algebras of higher operads as enriched categories

TL;DR

This paper explores the relationship between higher operads and enriched categories, establishing an equivalence between algebras of omega-operads and categories enriched in globular sets with lax monoidal structures.

Contribution

It introduces a correspondence between normalized omega-operads and lax monoidal structures on globular sets, linking their algebras to enriched categories.

Findings

Establishes a correspondence between omega-operads and lax monoidal structures.

Shows an equivalence between omega-operad algebras and enriched categories.

Provides a framework connecting higher operads with enriched category theory.

Abstract

We decribe the correspondence between normalised $\omega$-operads and certain lax monoidal structures on the category of globular sets. As with ordinary monoidal categories, one has a notion of category enriched in a lax monoidal category. Within the aforementioned correspondence, we provide also an equivalence between the algebras of a given normalised $\omega$-operad, and categories enriched in globular sets for the induced lax monoidal structure.