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arXiv · 2212.03146

Univalent Monoidal Categories

Kobe Wullaert·Ralph Matthes·Benedikt Ahrens
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Abstract

Univalent categories constitute a well-behaved and useful notion of category in univalent foundations. The notion of univalence has subsequently been generalized to bicategories and other structures in (higher) category theory. Here, we zoom in on monoidal categories and study them in a univalent setting. Specifically, we show that the bicategory of univalent monoidal categories is univalent. Furthermore, we construct a Rezk completion for monoidal categories: we show how any monoidal category is weakly equivalent to a univalent monoidal category, universally. We have fully formalized these results in UniMath, a library of univalent mathematics in the Coq proof assistant.

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Kobe Wullaert, Ralph Matthes, Benedikt Ahrens. 2022-12-06. Univalent Monoidal Categories. https://doi.org/10.4230/lipics.types.2022.15

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