Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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
   • CommentTimeDec 15th 2010
   • (edited Dec 15th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI worked a little on the entry [[separated presheaf]]. Apart from some general editing I * added construction and proof of the separafication functor; * began a section on the full notion of bi-separated presheaf. More deserves to be done here, but I have to stop for the moment.

   I worked a little on the entry separated presheaf. Apart from some general editing I

   • added construction and proof of the separafication functor;

   • began a section on the full notion of bi-separated presheaf.

   More deserves to be done here, but I have to stop for the moment.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeDec 15th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt would be good to move biseparated to a separate entry. It is a much more rarely used concept.

   It would be good to move biseparated to a separate entry. It is a much more rarely used concept.

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeJun 20th 2013
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAdded the remark that a constant sheaf on a site for which every covering family is inhabited is in fact separated (as per my recent MO question/answer).

   Added the remark that a constant sheaf on a site for which every covering family is inhabited is in fact separated (as per my recent MO question/answer).

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 20th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I have cross-lined a bit with _[[locally connected site]]_. If you find a minute, please consider either adding a pointer to the proof or the proof itself (simple as it may be, but for completeness).

   Thanks! I have cross-lined a bit with locally connected site.

   If you find a minute, please consider either adding a pointer to the proof or the proof itself (simple as it may be, but for completeness).

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMay 18th 2022
   • (edited Dec 15th 2022 by Urs)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: ### Examples [[Diffeological spaces]] are biseparated presheaves for the bisite structure on [[cartesian spaces]], where $J$ is the usual topology of open covers and $K$ is the topology given by the families $$\coprod_{u\in U}\mathbf{R}^0 \to U$$ for every [[cartesian space]] $U$. The [[sheaf]] condition with respect to $J$ yields a [[smooth set]], whereas the [[separated presheaf]] condition with respect to $K$ makes it into a [[diffeological space]]. <a href="https://ncatlab.org/nlab/revision/diff/separated+presheaf/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/separated+presheaf/18">v18</a>, <a href="https://ncatlab.org/nlab/show/separated+presheaf">current</a>

   Added:

   Examples

   Diffeological spaces are biseparated presheaves for the bisite structure on cartesian spaces, where $J$ is the usual topology of open covers and $K$ is the topology given by the families

   $$\coprod_{u\in U}\mathbf{R}^0 \to U$$

   for every cartesian space $U$.

   The sheaf condition with respect to $J$ yields a smooth set, whereas the separated presheaf condition with respect to $K$ makes it into a diffeological space.

   diff, v18, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 19th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added ([here](https://ncatlab.org/nlab/show/separated+presheaf#DiffeologicalSpaces)) an Examples-environment and fixed the broken link to diffeological spaces. <a href="https://ncatlab.org/nlab/revision/diff/separated+presheaf/19">diff</a>, <a href="https://ncatlab.org/nlab/revision/separated+presheaf/19">v19</a>, <a href="https://ncatlab.org/nlab/show/separated+presheaf">current</a>

   I have added (here) an Examples-environment and fixed the broken link to diffeological spaces.

   diff, v19, current

7. • CommentRowNumber7.
   • CommentAuthorvarkor
   • CommentTimeDec 14th 2022
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdded a reference to [[epipresheaf]]. <a href="https://ncatlab.org/nlab/revision/diff/separated+presheaf/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/separated+presheaf/21">v21</a>, <a href="https://ncatlab.org/nlab/show/separated+presheaf">current</a>

   Added a reference to epipresheaf.

   diff, v21, current