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 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 sheaves 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
   • CommentTimeJul 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexTodd has added to [[Grothendieck topos]] the statement and proof that any such is total and cototal (and I have added to [[adjoint functor theorem]] the statement that this implies that all (co)limit preserving functors between sheaf toposes have (right)left adjoints). I notice that we should really merge [[Grothendieck topos]] with [[category of sheaves]]. But I don't have the energy to do this now.

   Todd has added to Grothendieck topos the statement and proof that any such is total and cototal (and I have added to adjoint functor theorem the statement that this implies that all (co)limit preserving functors between sheaf toposes have (right)left adjoints).

   I notice that we should really merge Grothendieck topos with category of sheaves. But I don’t have the energy to do this now.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 28th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI would watch out about that merge, because "sheaf" need not mean a set-valued sheaf.

   I would watch out about that merge, because “sheaf” need not mean a set-valued sheaf.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThat's true. But maye that's one more reason to merge the content from [[category of sheaves]] into [[Grothendieck topos]]: because currently that's all about set-valued sheaves.

   That’s true. But maye that’s one more reason to merge the content from category of sheaves into Grothendieck topos: because currently that’s all about set-valued sheaves.

4. • CommentRowNumber4.
   • CommentAuthorTodd_Trimble
   • CommentTimeJul 28th 2011
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexWell, I just added a few words (in the Idea section) to [[presheaf]] to the effect that historically, the focus on set-valued sheaves came later, after all the developments in the 40's and 50's on things like sheaves of abelian groups. I think you have a point, but I'd like to think about it some more.

   Well, I just added a few words (in the Idea section) to presheaf to the effect that historically, the focus on set-valued sheaves came later, after all the developments in the 40’s and 50’s on things like sheaves of abelian groups. I think you have a point, but I’d like to think about it some more.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, sure, we should do it correctly. We should keep both entries seperate. But it would be good not to spread out the material about sheaf toposes in two places in two parallel ways.

   Okay, sure, we should do it correctly. We should keep both entries seperate. But it would be good not to spread out the material about sheaf toposes in two places in two parallel ways.