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arXiv · 2601.03985

Boardman-Vogt tensor product and wreath product of operadic categories

Daria Pavlova
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Abstract

We introduce the wreath product of operadic categories and show that it produces a monoidal structure on the category OpCat of strict operadic categories. We relate the wreath product to the well known Boardman-Vogt tensor product of operads by interpreting the category of symmetric set-valued colored unital operads as a reflexive subcategory of OpCat. Our main result is that the reflection is a strong monoidal functor. In particular, the Boardman-Vogt tensor product of two colored operads in Set is isomorphic to an operad that is induced by the wreath product of suitable operadic categories.

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Daria Pavlova. 2026-01-07. Boardman-Vogt tensor product and wreath product of operadic categories. https://arxiv.org/abs/2601.03985

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