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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.
   • CommentAuthorUrs
   • CommentTimeJan 20th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have started working on [[Diff]]: added a subsection with discussion of its properties as a site. Added statement and proof of the fact that * $Sh(Diff)$ is a [[cohesive topos]] (direct consequence of the _comparison lemma_) * $Sh_{(\infty,1)}(Diff)$ is a [[cohesive (infinity,1)-topos]] (easy with some lemmas from the literature, but not immediate (I think))

   I have started working on Diff: added a subsection with discussion of its properties as a site.

   Added statement and proof of the fact that

   • $Sh(Diff)$ is a cohesive topos (direct consequence of the comparison lemma)

   • $Sh_{(\infty,1)}(Diff)$ is a cohesive (infinity,1)-topos (easy with some lemmas from the literature, but not immediate (I think))

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 29th 2020
   • (edited May 29th 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI renamed this entry from "Diff" to "SmoothManifolds", with a discussion of alternative terminology in the text. This is to avoid clashes with other usages of "[[Diff]]" (which I made now a disambiguation page). <a href="https://ncatlab.org/nlab/revision/diff/SmoothManifolds/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/SmoothManifolds/16">v16</a>, <a href="https://ncatlab.org/nlab/show/SmoothManifolds">current</a>

   I renamed this entry from “Diff” to “SmoothManifolds”, with a discussion of alternative terminology in the text. This is to avoid clashes with other usages of “Diff” (which I made now a disambiguation page).

   diff, v16, current