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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/symmetric+monoidal+groupoid/1">v1</a>, <a href="https://ncatlab.org/nlab/show/symmetric+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 there was no particular reason not to say that a symmetric monoidal groupoid is a symmetric monoidal category which happens to be a groupoid, I have slightly expanded and adjusted the Idea-paragraph 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 [[braided monoidal groupoid]] whose dagger adjoint of the [[braiding]] is the opposite [[braiding]], > Equivalently, a [[1-type|1-truncated]] [[En-algebra|$E_3$-space]] or [[E-infinity algebra|$E_\infty$-space]]. <a href="https://ncatlab.org/nlab/revision/diff/symmetric+monoidal+groupoid/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/symmetric+monoidal+groupoid/3">v3</a>, <a href="https://ncatlab.org/nlab/show/symmetric+monoidal+groupoid">current</a>

   Assuming that there was no particular reason not to say that a symmetric monoidal groupoid is a symmetric monoidal category which happens to be a groupoid, I have slightly expanded and adjusted the Idea-paragraph 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 braided monoidal groupoid whose dagger adjoint of the braiding is the opposite braiding,

   Equivalently, a 1-truncated $E_3$-space or $E_\infty$-space.

   diff, v3, current