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

(0 1)-category-theory 2-category 2-category-theory 2-monad abelian-categories accessible adjoint algebra algebraic algebraic-geometry analysis arithmetic beauty book bug bundle categories category category-theory chern-simons-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry conference connection constructive constructive-mathematics cosmology database deformation-theory descent differential differential-cohomology differential-geometry duality enriched enriched-category-theory enrichment examples factorization-system fiber fibration forms foundation foundations functional-analysis functor galois-theory gauge-theory gebra general topology geometric geometric-quantization geometry gravity group-theory higher higher-algebra higher-category-theory higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory homtopy-type-theory infinity-groupoid integration-theory internal-categories kan lie lie-algebras lie-theory limit limits linear linear-algebra locale localization localization-theory logic manifolds mathematics measure measure-theory mechanics meta modal-logic model model-category-theory monoidal monoidal-category monoidal-category-theory morphism n-groups newpage noncommutative noncommutative-geometry object operator operator-algebra order-theory philosophy physics predicative pretopology pro-object probability-theory quantum quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry set set-theory sheaf simplicial site space stable-homotopy-theory stack string string-theory subobject supergeometry symplectic-geometry tannaka tensor terminology theory topologica-quantum-field-theory topology topos topos-theory torsor tqft type type-theory universal weighted-limit

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated _[[internal sheaf]]_ Mainly it was bugging me that I didn't find a piece of literature that said it quite explicitly the way I do there, so I wanted to have that written down. To be expanded, eventually.

   created internal sheaf

   Mainly it was bugging me that I didn’t find a piece of literature that said it quite explicitly the way I do there, so I wanted to have that written down. To be expanded, eventually.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2012
   • (edited Mar 16th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have further expanded [[internal sheaf|it]] (added two basic Propositions, more details in the definitions) and tried to prettify a bit more.

   I have further expanded it (added two basic Propositions, more details in the definitions) and tried to prettify a bit more.

3. • CommentRowNumber3.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeAug 29th 2012
   • PermaLink
   Author: IngoBlechschmidt
   Format: MarkdownItexI added the pedestrian definitions of _presheaf_ and _sheaf_ (as internal diagrams).

   I added the pedestrian definitions of presheaf and sheaf (as internal diagrams).

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeAug 29th 2012
   • (edited Aug 29th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I moved your new paragraph to become a subsection of the Definition-section, made my previous material there also a subsection, and added at the beginning of the Definition-section a little lead-in on how we will present two versions of the definition, one abstract, one more explicit. Of course much of the explicitness of the second definition (the one you added) is out-sourced to the entry _[[internal diagram]]_- But I guess that's okay.

   Thanks!

   I moved your new paragraph to become a subsection of the Definition-section, made my previous material there also a subsection, and added at the beginning of the Definition-section a little lead-in on how we will present two versions of the definition, one abstract, one more explicit.

   Of course much of the explicitness of the second definition (the one you added) is out-sourced to the entry internal diagram- But I guess that’s okay.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 30th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn this spirit I have also edited the very very last sentence of the entry (at then end of the References) making it now point to the two Definition-sections where previously it just vaguely referred to the explicit defintition. Good.

   In this spirit I have also edited the very very last sentence of the entry (at then end of the References) making it now point to the two Definition-sections where previously it just vaguely referred to the explicit defintition. Good.

6. • CommentRowNumber6.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeAug 30th 2012
   • PermaLink
   Author: IngoBlechschmidt
   Format: MarkdownItexThanks, much better! I agree it's not a problem that the actual explicitness is one further click away.

   Thanks, much better! I agree it’s not a problem that the actual explicitness is one further click away.

7. • CommentRowNumber7.
   • CommentAuthorzskoda
   • CommentTimeSep 7th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexDo you see a direct way to expand the concept to an internal generalization of non-set valued sheaves ? In my understanding this entry generalizes the set-valued sheaves only.

   Do you see a direct way to expand the concept to an internal generalization of non-set valued sheaves ? In my understanding this entry generalizes the set-valued sheaves only.

8. • CommentRowNumber8.
   • CommentAuthorIngoBlechschmidt
   • CommentTimeSep 8th 2012
   • PermaLink
   Author: IngoBlechschmidt
   Format: MarkdownItexYou can certainly have presheaves valued in locally internal categories over the base topos, see the last section of _[[internal diagram]]_ (where this is detailed in the language of indexed categories). Using the internal language, these look exactly like ordinary non-Set-valued presheaves; so I'd guess that to obtain a sensible notion of a sheaf, one could simply formulate the usual sheaf condition in the internal language.

   You can certainly have presheaves valued in locally internal categories over the base topos, see the last section of internal diagram (where this is detailed in the language of indexed categories). Using the internal language, these look exactly like ordinary non-Set-valued presheaves; so I’d guess that to obtain a sensible notion of a sheaf, one could simply formulate the usual sheaf condition in the internal language.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeSep 8th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe formulation [In terms of external 2-sheaves](http://ncatlab.org/nlab/show/internal%20sheaf#InTermsOf2Sheaves) works by passing to the 2-category of internal categories. In there you can do all of category theory and topos theory as you did externally.

   The formulation In terms of external 2-sheaves works by passing to the 2-category of internal categories. In there you can do all of category theory and topos theory as you did externally.