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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 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.
   • CommentAuthorUrs
   • CommentTimeFeb 3rd 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * [[Arthur Parzygnat]], _Two-dimensional algebra in lattice gauge theory_ ([arXiv:1802.01139](https://arxiv.org/abs/1802.01139)) which provides a wealth of computational details and illustrative graphics. <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/24">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/24">v24</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   added pointer to

   • Arthur Parzygnat, Two-dimensional algebra in lattice gauge theory (arXiv:1802.01139)

   which provides a wealth of computational details and illustrative graphics.

   diff, v24, current

2. • CommentRowNumber2.
   • CommentAuthorAli Caglayan
   • CommentTimeFeb 3rd 2019
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexThat is a very fun paper!

   That is a very fun paper!

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 30th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexfixed a bunch of broken links <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/25">v25</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   fixed a bunch of broken links

   diff, v25, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for: * [[Arthur Parzygnat]], _Two-dimensional algebra in lattice gauge theory_, Journal of Mathematical Physics 60, 043506 (2019) ([arXiv:1802.01139](https://arxiv.org/abs/1802.01139), [doi:10.1063/1.5078532](https://doi.org/10.1063/1.5078532)) <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/27">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/27">v27</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   added publication data for:

   • Arthur Parzygnat, Two-dimensional algebra in lattice gauge theory, Journal of Mathematical Physics 60, 043506 (2019) (arXiv:1802.01139, doi:10.1063/1.5078532)

   diff, v27, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJun 29th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Lukas Müller]], [[Lukas Woike]], *Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field Theory*, J. Homotopy Relat. Struct. **15** (2020) 113–142 &lbrack;[arXiv:1802.10455](https://arxiv.org/abs/1802.10455), [doi:10.1007/s40062-019-00242-3](https://doi.org/10.1007/s40062-019-00242-3)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/30">v30</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   added pointer to:

   • Lukas Müller, Lukas Woike, Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field Theory, J. Homotopy Relat. Struct. 15 (2020) 113–142 [arXiv:1802.10455, doi:10.1007/s40062-019-00242-3]

   diff, v30, current

6. • CommentRowNumber6.
   • CommentAuthorjim stasheff
   • CommentTimeOct 23rd 2023
   • PermaLink
   Author: jim stasheff
   Format: MarkdownItexHave added two lines of Tex words missing just before flat equivalences between these fibers to paths in $\Sigma$, and so on makes sense for ordinary bundles <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/31">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/31">v31</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   Have added two lines of Tex words missing just before flat

   equivalences between these fibers to paths in $\Sigma$, and so on makes sense for ordinary bundles

   diff, v31, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeOct 23rd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe answer to the question is "Yes." I have rolled back your edit. Questions are best asked here in forum comments.

   The answer to the question is “Yes.”

   I have rolled back your edit. Questions are best asked here in forum comments.

8. • CommentRowNumber8.
   • CommentAuthorUrs
   • CommentTimeJul 3rd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Konrad Waldorf]], *Parallel transport in principal 2-bundles*, Higher Structures **2** 1 (2018) 57-115 &lbrack;[arXiv:1704.08542](https://arxiv.org/abs/1704.08542), [pdf](https://higher-structures.math.cas.cz/api/files/issues/Vol2Iss1/Waldorf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/35">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/35">v35</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   added pointer to:

   • Konrad Waldorf, Parallel transport in principal 2-bundles, Higher Structures 2 1 (2018) 57-115 [arXiv:1704.08542, pdf]

   diff, v35, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeAug 9th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * Nino Scalbi: *Differential Cohomology as Diffeological Homotopy Theory* &lbrack;[arXiv:2408.02593](https://arxiv.org/abs/2408.02593)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/36">v36</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

   added pointer to:

   • Nino Scalbi: Differential Cohomology as Diffeological Homotopy Theory [arXiv:2408.02593]

   diff, v36, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexam adding a few more references, such as * [[João Faria Martins]], [[Roger Picken]]: *Surface holonomy for non-abelian 2-bundles via double groupoids*, Advances in Mathematics **226** 4 (2011) 3309-3366 \[<a href="https://doi.org/10.1016/j.aim.2010.10.017">doi:10.1016/j.aim.2010.10.017</a>\] * [[Amnon Yekutieli]]: *Nonabelian Multiplicative Integration on Surfaces*, World Scientific (2015) &lbrack;[arXiv:1007.1250](https://arxiv.org/abs/1007.1250), [doi:10.1142/9537](https://doi.org/10.1142/9537)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/37">v37</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

    am adding a few more references, such as

    • João Faria Martins, Roger Picken: Surface holonomy for non-abelian 2-bundles via double groupoids, Advances in Mathematics 226 4 (2011) 3309-3366 [doi:10.1016/j.aim.2010.10.017]

    • Amnon Yekutieli: Nonabelian Multiplicative Integration on Surfaces, World Scientific (2015) [arXiv:1007.1250, doi:10.1142/9537]

    diff, v37, current

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2024
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded pointer to: * Ilya Chevyrev, [[Joscha Diehl]], [[Kurusch Ebrahimi-Fard]], Nikolas Tapia: *A multiplicative surface signature through its Magnus expansion* &lbrack;[arXiv:2406.16856](https://arxiv.org/abs/2406.16856)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/higher+parallel+transport/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/higher+parallel+transport/38">v38</a>, <a href="https://ncatlab.org/nlab/show/higher+parallel+transport">current</a>

    added pointer to:

    • Ilya Chevyrev, Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia: A multiplicative surface signature through its Magnus expansion [arXiv:2406.16856]

    diff, v38, current