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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/braided+monoidal+groupoid/1">v1</a>, <a href="https://ncatlab.org/nlab/show/braided+monoidal+groupoid">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexAssuming that you did not have a particular reason not to say that a braided monoidal groupoid is a braided monoidal category which happens to be a groupoid, I have slightly expanded and adjusted the Idea-section to the following: > A *braided monoidal groupoid* is a [[braided monoidal category]] whose underlying [[category]] happens to be a [[groupoid]] (hence all whose [[morphisms]] are [[isomorphisms]].) > Equivalently: A [[monoidal groupoid]] with [[braiding]] that satisfies the [[hexagon identities]], > Equivalently: a [[1-type|1-truncated]] [[En-algebra|$E_2$-space]]. <a href="https://ncatlab.org/nlab/revision/diff/braided+monoidal+groupoid/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/braided+monoidal+groupoid/3">v3</a>, <a href="https://ncatlab.org/nlab/show/braided+monoidal+groupoid">current</a>

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

   A braided monoidal groupoid is a braided monoidal category whose underlying category happens to be a groupoid (hence all whose morphisms are isomorphisms.)

   Equivalently: A monoidal groupoid with braiding that satisfies the hexagon identities,

   Equivalently: a 1-truncated $E_2$-space.

   diff, v3, current