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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 nlab noncommutative noncommutative-geometry number-theory object 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
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexcopied reference from HoTT wiki Anonymous <a href="https://ncatlab.org/nlab/revision/Higher+Groups+in+Homotopy+Type+Theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Higher+Groups+in+Homotopy+Type+Theory">current</a>

   copied reference from HoTT wiki

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have made the requested *[[higher groups]]* redirect to the existing entry *[[n-groups]]*. Then I have hyperlinked *[[infinity-groups]]*, which certainly exists. Also link for *[[connective spectrum]]*. By the way, to make good use of all these new `category:reference`entries, one should point to them from where the articles are being referenced. I have done so now [here](https://ncatlab.org/nlab/show/infinity-group#BuchholtzDoornRijke18). <a href="https://ncatlab.org/nlab/revision/diff/Higher+Groups+in+Homotopy+Type+Theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Higher+Groups+in+Homotopy+Type+Theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Higher+Groups+in+Homotopy+Type+Theory">current</a>

   I have made the requested higher groups redirect to the existing entry n-groups.

   Then I have hyperlinked infinity-groups, which certainly exists.

   Also link for connective spectrum.

   By the way, to make good use of all these new category:referenceentries, one should point to them from where the articles are being referenced. I have done so now here.

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexBy the way, we do have an entry *[[delooping]]*. We did not have the requested *[[delooped]]* as a redirect. I have made it a redirect now, but best to link to standard word form, since we can't possibly pre-empt all variations as redirects.

   By the way, we do have an entry delooping. We did not have the requested delooped as a redirect.

   I have made it a redirect now, but best to link to standard word form, since we can’t possibly pre-empt all variations as redirects.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn adding the missing publication data, I have taken the liberty of reformatting a litte. Does it not look much better this way: *** * [[Ulrik Buchholtz]], [[Floris van Doorn]], [[Egbert Rijke]]: **Higher Groups in Homotopy Type Theory** LICS '18: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science [arXiv:1802.04315](https://arxiv.org/abs/1802.04315) [doi:10.1145/3209108.3209150](https://doi.org/10.1145/3209108.3209150) on [[infinity-groups]] in [[homotopy type theory]]. > **Abtract.** We present a development of the theory of [[higher groups]], including [[infinity-groups]] and [[connective spectra|connective]] [[spectra]], in [[homotopy type theory]]. An [[infinity-group|infinity group]] is simply the [[loops]] in a [[pointed]], [[connected]] [[type]], where the [[group]] structure comes from the structure inherent in the [[identity types]] of [[Martin-Löf type theory]]. We investigate ordinary [[groups]] from this viewpoint, as well as [[n-group|higher dimensional groups]] and groups that can be [[delooped]] more than once. A major result is the stabilization theorem, which states that if an [[n-type]] can be [[delooped]] $n+2$ times, then it is an [[infinite loop space|infinite loop type]]. Most of the results have been formalized in the [[Lean]] [[proof assistant]]. *** ? <a href="https://ncatlab.org/nlab/revision/diff/Higher+Groups+in+Homotopy+Type+Theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Higher+Groups+in+Homotopy+Type+Theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Higher+Groups+in+Homotopy+Type+Theory">current</a>

   In adding the missing publication data, I have taken the liberty of reformatting a litte.

   Does it not look much better this way:

   ---

   • Ulrik Buchholtz, Floris van Doorn, Egbert Rijke:

     Higher Groups in Homotopy Type Theory

     LICS ’18:

     Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

     arXiv:1802.04315

     doi:10.1145/3209108.3209150

   on infinity-groups in homotopy type theory.

   Abtract. We present a development of the theory of higher groups, including infinity-groups and connective spectra, in homotopy type theory. An infinity group is simply the loops in a pointed, connected type, where the group structure comes from the structure inherent in the identity types of Martin-Löf type theory. We investigate ordinary groups from this viewpoint, as well as higher dimensional groups and groups that can be delooped more than once. A major result is the stabilization theorem, which states that if an n-type can be delooped $n+2$ times, then it is an infinite loop type. Most of the results have been formalized in the Lean proof assistant.

   ---

   ?

   diff, v2, current