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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 infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic manifolds 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 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. • CommentRowNumber101.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 21st 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexOk, with your encouragement I'll give it a go.

   Ok, with your encouragement I’ll give it a go.

2. • CommentRowNumber102.
   • CommentAuthorDavid_Corfield
   • CommentTimeFeb 25th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexPeter Scholze has replied to my [MO question](https://mathoverflow.net/q/384318/447). That's right my response that a stable object in a $\infty$-topos that is relative cohesive over condensed $\infty$-groupoids (or pyknotic ones anyway) should generate a fracture square?

   Peter Scholze has replied to my MO question. That’s right my response that a stable object in a $\infty$-topos that is relative cohesive over condensed $\infty$-groupoids (or pyknotic ones anyway) should generate a fracture square?

3. • CommentRowNumber103.
   • CommentAuthorUrs
   • CommentTimeMar 9th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded brief commentary around the references by Schwede (suggesting regarding orbifold cohomology in global homotopy theory) and Juran (spellign it out) <a href="https://ncatlab.org/nlab/revision/diff/orbifold+cohomology/42">diff</a>, <a href="https://ncatlab.org/nlab/revision/orbifold+cohomology/42">v42</a>, <a href="https://ncatlab.org/nlab/show/orbifold+cohomology">current</a>

   added brief commentary around the references by Schwede (suggesting regarding orbifold cohomology in global homotopy theory) and Juran (spellign it out)

   diff, v42, current

4. • CommentRowNumber104.
   • CommentAuthorUrs
   • CommentTimeOct 26th 2021
   • (edited Oct 26th 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have removed the bulk of the entry, since that was a set of notes which has meanwhile evolved into polished form in [arXiv:2008.01101](https://arxiv.org/abs/2008.01101), while what remained here had meanwhile become notationally inconsistent with both that and related $n$Lab entries, to the extent that it now would have been serious work to adjust notation. So I just removed it for the time being, but added more prominent cross-links with the new entries *[[singular cohesion]]* and [[singular-smooth infinity-groupoid]]. <a href="https://ncatlab.org/nlab/revision/diff/orbifold+cohomology/44">diff</a>, <a href="https://ncatlab.org/nlab/revision/orbifold+cohomology/44">v44</a>, <a href="https://ncatlab.org/nlab/show/orbifold+cohomology">current</a>

   I have removed the bulk of the entry, since that was a set of notes which has meanwhile evolved into polished form in arXiv:2008.01101, while what remained here had meanwhile become notationally inconsistent with both that and related $n$Lab entries, to the extent that it now would have been serious work to adjust notation.

   So I just removed it for the time being, but added more prominent cross-links with the new entries singular cohesion and singular-smooth infinity-groupoid.

   diff, v44, current