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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 25th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItex_[[braided 2-group]]_

   braided 2-group

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded more original references: *** Under the name "braided gr-categories" or "braided cat-groups" and thought of as a sub-class of [[braided monoidal categories]], the notion of braided 2-groups is considered in: * [[M. Bullejos]], [[Pilar Carrasco]], [[Antonio M. Cegarra]], *Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg–MacLane's classification theorem*, Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 163 - 189 ([doi:10.1017/S0305004100071498](https://doi.org/10.1017/S0305004100071498)) * [[Antonio R. Garzón]], Jesus G Miranda, *Homotopy theory for (braided) cat-groups*, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) no. 2, pp. 99-139 ([numdam:CTGDC_1997__38_2_99_0](http://www.numdam.org/item/?id=CTGDC_1997__38_2_99_0)) * [[Vladimir Drinfeld]], [[Shlomo Gelaki]], [[Dmitri Nikshych]], [[Victor Ostrik]], Appendix E of: *On braided fusion categories I*, Selecta Mathematica. New Series 16 (2010), no. 1, 1–119 ([doi:10.1007/s00029-010-0017-z](https://doi.org/10.1007/s00029-010-0017-z)) In the generality of [[braided ∞-group|braided ∞-group stacks]] that are [[iterated loop space|double loopings]], the notion is made explicit in: * [[Thomas Nikolaus]], [[Urs Schreiber]], [[Danny Stevenson]], Def. 4.28 of: _[[schreiber:Principal ∞-bundles -- theory, presentations and applications|Principal ∞-bundles -- General theory]]_, Journal of Homotopy and Related Structures, Volume 10, Issue 4 (2015), pages 749-801 ([doi:10.1007/s40062-014-0083-6](http://link.springer.com/article/10.1007/s40062-014-0083-6), [arXiv:1207.0248](http://arxiv.org/abs/1207.0248)) *** <a href="https://ncatlab.org/nlab/revision/diff/braided+2-group/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/braided+2-group/3">v3</a>, <a href="https://ncatlab.org/nlab/show/braided+2-group">current</a>

   Added more original references:

   ---

   Under the name “braided gr-categories” or “braided cat-groups” and thought of as a sub-class of braided monoidal categories, the notion of braided 2-groups is considered in:

   • M. Bullejos, Pilar Carrasco, Antonio M. Cegarra, Cohomology with coefficients in symmetric cat-groups. An extension of Eilenberg–MacLane’s classification theorem, Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 163 - 189 (doi:10.1017/S0305004100071498)

   • Antonio R. Garzón, Jesus G Miranda, Homotopy theory for (braided) cat-groups, Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 38 (1997) no. 2, pp. 99-139 (numdam:CTGDC_1997__38_2_99_0)

   • Vladimir Drinfeld, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik, Appendix E of: On braided fusion categories I, Selecta Mathematica. New Series 16 (2010), no. 1, 1–119 (doi:10.1007/s00029-010-0017-z)

   In the generality of braided ∞-group stacks that are double loopings, the notion is made explicit in:

   • Thomas Nikolaus, Urs Schreiber, Danny Stevenson, Def. 4.28 of: Principal ∞-bundles – General theory, Journal of Homotopy and Related Structures, Volume 10, Issue 4 (2015), pages 749-801 (doi:10.1007/s40062-014-0083-6, arXiv:1207.0248)

   ---

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2021
   • (edited Jul 21st 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso: *** As a special case of [[k-tuply groupal n-groupoids]]: * [[Antonio R. Garzón]], Jesus G. Miranda, Section 6 of: _Serre homotopy theory in subcategories of simplicial groups_, Journal of Pure and Applied Algebra Volume 147, Issue 2, 24 March 2000, Pages 107-123 (<a href="https://doi.org/10.1016/S0022-4049(98)00143-1">doi:10.1016/S0022-4049(98)00143-1</a>) *** <a href="https://ncatlab.org/nlab/revision/diff/braided+2-group/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/braided+2-group/3">v3</a>, <a href="https://ncatlab.org/nlab/show/braided+2-group">current</a>

   also:

   ---

   As a special case of k-tuply groupal n-groupoids:

   • Antonio R. Garzón, Jesus G. Miranda, Section 6 of: Serre homotopy theory in subcategories of simplicial groups, Journal of Pure and Applied Algebra Volume 147, Issue 2, 24 March 2000, Pages 107-123 (doi:10.1016/S0022-4049(98)00143-1)

   ---

   diff, v3, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 21st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexalso pointer to: * [[André Joyal]], [[Ross Street]], Section 3 of: _Braided tensor categories_, Adv. Math. **102** (1993), 20--78 ([doi:10.1006/aima.1993.1055](https://doi.org/10.1006/aima.1993.1055)) <a href="https://ncatlab.org/nlab/revision/diff/braided+2-group/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/braided+2-group/4">v4</a>, <a href="https://ncatlab.org/nlab/show/braided+2-group">current</a>

   also pointer to:

   • André Joyal, Ross Street, Section 3 of: Braided tensor categories, Adv. Math. 102 (1993), 20–78 (doi:10.1006/aima.1993.1055)

   diff, v4, current