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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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 3rd 2017
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   Author: David_Corfield
   Format: MarkdownItexDid you see [Relationship between synthetic differential geometry and differential cohesion?](https://mathoverflow.net/q/278929/447), Urs?

   Did you see Relationship between synthetic differential geometry and differential cohesion?, Urs?

2. • CommentRowNumber2.
   • CommentAuthormaxsnew
   • CommentTimeSep 3rd 2017
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   Author: maxsnew
   Format: TextHope I didn't mess up the answer too badly :)

   Hope I didn't mess up the answer too badly :)
3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 4th 2017
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   Author: Urs
   Format: MarkdownItexDavid, thanks for the alert! Max, thanks for the reply, that looks good.

   David, thanks for the alert! Max, thanks for the reply, that looks good.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeSep 4th 2017
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   Author: David_Corfield
   Format: MarkdownItexI just added a couple of comments. I thought your name should at least appear on that page. Taking a look at that [Differential Cohesive Type Theory (Extended Abstract)](https://hott-uf.github.io/2017/abstracts/cohesivett.pdf), I'd have thought there ought to be clearer attribution of ideas. Someone reading that second paragraph could easily be misled into thinking that differential cohesion was up and running at least as far back as 1997.

   I just added a couple of comments. I thought your name should at least appear on that page.

   Taking a look at that Differential Cohesive Type Theory (Extended Abstract), I’d have thought there ought to be clearer attribution of ideas. Someone reading that second paragraph could easily be misled into thinking that differential cohesion was up and running at least as far back as 1997.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeSep 4th 2017
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   Author: Urs
   Format: MarkdownItexRight; in the strict sense of the word, the way I introduced it in "Differential cohomology in a cohesive $\infty$-topos", _differential cohesion_ is a system of six modalities, three for cohesion, three for its differential refinement, together with their adjointness relation and the requirement that $shape \lt \Im$. While the latter three modalities in isolation may be matched to what Simpson-Teleman consider in "De Rham theorem for $\infty$-stacks", their algebro geometric context is not cohesive and hence not "differentially cohesive" in the strict sense.

   Right; in the strict sense of the word, the way I introduced it in “Differential cohomology in a cohesive $\infty$-topos”, differential cohesion is a system of six modalities, three for cohesion, three for its differential refinement, together with their adjointness relation and the requirement that $shape \lt \Im$. While the latter three modalities in isolation may be matched to what Simpson-Teleman consider in “De Rham theorem for $\infty$-stacks”, their algebro geometric context is not cohesive and hence not “differentially cohesive” in the strict sense.