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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 16th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/monoidal+groupoid/1">v1</a>, <a href="https://ncatlab.org/nlab/show/monoidal+groupoid">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2022
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   Author: Urs
   Format: MarkdownItexAssuming 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 [[A4-spatial groupoid|$A_4$-spatial groupoid]] whose [[unitors]] satisfy the [[triangle identities]]; > Equivalently: a [[1-type|1-truncated]] [[A-infinity space|$A_\infty$-space]]/[[En-algebra|$E_1$-space]]. also cross-linked with *[[Picard groupoid]]* <a href="https://ncatlab.org/nlab/revision/diff/monoidal+groupoid/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/monoidal+groupoid/3">v3</a>, <a href="https://ncatlab.org/nlab/show/monoidal+groupoid">current</a>

   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;

   Equivalently: a 1-truncated $A_\infty$-space/$E_1$-space.

   also cross-linked with Picard groupoid

   diff, v3, current