Boardman-Vogt tensor product, wreath product, operadic categories

TL;DR

This paper introduces a wreath product for operadic categories and uses it to establish an explicit isomorphism between the Boardman-Vogt tensor product of colored operads and an operad derived from the wreath product, advancing operad theory.

Contribution

It defines a new wreath product for operadic categories and connects it to the Boardman-Vogt tensor product, providing a novel structural insight.

Findings

Established an explicit isomorphism between tensor and wreath product-based operads.

Extended operadic constructions to include a new wreath product framework.

Provided tools for analyzing operad combinations via operadic Grothendieck constructions.

Abstract

We introduce the wreath product for a class of operadic categories and use it to construct an explicit isomorphism between the Boardman-Vogt tensor product of two colored operads in Set and an operad induced by the wreath product of operadic Grothendieck constructions of the respective operads.