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Anonymous

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 16th 2022

Assuming that you didn’t have a particular reason not to say that a monoidal groupoid is a monoidal category that happens to be a groupoid, I have slightly expanded and adjusted the Idea-section to the following:

A monoidal category whose underlying category is a groupoid (hence all whose morphisms are invertible).

Equivalently: an $A_4$-spatial groupoid whose unitors satisfy the triangle identities;