Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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
   • PermaLink
   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