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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 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 sheaves 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.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 16th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIs that a deliberate policy to give titles of HoTT reconstructions of maths as 'X in Homotopy Type Theory'? Easy to collect articles if so. * Covering Spaces in Homotopy Type Theory, unpublished * Higher Groups in Homotopy Type Theory, arXiv:1802.04315, * Free Higher Groups in Homotopy Type Theory, arXiv:1805.02069 * Localization in Homotopy Type Theory, arXiv:1807.04155 * The James construction and $\pi_4(S^3)$ in homotopy type theory, arXiv: 1610.01134 * The Cayley-Dickson Construction in Homotopy Type Theory, arXiv:1610.01134 * Cellular Cohomology in Homotopy Type Theory, arXiv:1802.02191 * The real projective spaces in homotopy type theory, arXiv:1704.05770 * Synthetic Homology in Homotopy Type Theory, arXiv:1706.01540 * On the homotopy groups of spheres in homotopy type theory, arXiv:1606.05916 * A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory, arXiv:1605.03227 I'm being asked what has been achieved in this regard so far.

   Is that a deliberate policy to give titles of HoTT reconstructions of maths as ’X in Homotopy Type Theory’? Easy to collect articles if so.

   • Covering Spaces in Homotopy Type Theory, unpublished
   • Higher Groups in Homotopy Type Theory, arXiv:1802.04315,
   • Free Higher Groups in Homotopy Type Theory, arXiv:1805.02069
   • Localization in Homotopy Type Theory, arXiv:1807.04155
   • The James construction and $\pi_4(S^3)$ in homotopy type theory, arXiv: 1610.01134
   • The Cayley-Dickson Construction in Homotopy Type Theory, arXiv:1610.01134
   • Cellular Cohomology in Homotopy Type Theory, arXiv:1802.02191
   • The real projective spaces in homotopy type theory, arXiv:1704.05770
   • Synthetic Homology in Homotopy Type Theory, arXiv:1706.01540
   • On the homotopy groups of spheres in homotopy type theory, arXiv:1606.05916
   • A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory, arXiv:1605.03227

   I’m being asked what has been achieved in this regard so far.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeAug 16th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexIt seems to be fairly common. I suppose it's not a bad way to indicate that a paper is doing something that's "old" in classical algebraic topology, but "new" when done in HoTT.

   It seems to be fairly common. I suppose it’s not a bad way to indicate that a paper is doing something that’s “old” in classical algebraic topology, but “new” when done in HoTT.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeAug 16th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIt's a good idea. I'd encourage it. It makes it very easy to track down papers.

   It’s a good idea. I’d encourage it. It makes it very easy to track down papers.