Mario Román


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Gray monoid

Last updated May 18, 2023

A Gray monoid is a Gray category with a single object. They are a semistrict version of monoidal bicategories.

Gray monoids are 2-categories with associative and unital monoidal product $(\otimes)$, which however fails to be a 2-functor (see Monoidal Bicategories and Hopf Algebroids (Day, Street, 1997)). When working with monoidal bicategories, we can safely assume we are working with Gray monoids, as there is a coherence result.