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 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
   • CommentTimeJul 7th 2011
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIn the doctine [page](http://ncatlab.org/johnbaez/show/Doctrines) of John's web, it says >Categorified Gabriel–Ulmer duality is all about recovering the syntactic doctrine from the semantic doctrine. It struck me that 'recovering' is the kind of term you hear when people talk about [Tannaka](http://ncatlab.org/nlab/show/Tannaka+duality) reconstruction theorems. Looking at the page - [[reconstruction theorem]] - I see it includes both Tannakian examples and [[Lawvere's reconstruction theorem]], an ancestor of [[Gabriel-Ulmer duality]]. So I wondered if we ever have Gabriel-Ulmer and Tannaka duality treated together, and found Brian Day in [Enriched Tannaka reconstruction](http://www.sciencedirect.com/science/article/pii/0022404995000399) writing >Our approach provides a synthesis of Tannaka reconstruction and Gabriel-Ulmer duality. I can see how they're both reconstructing something by looking at the collection of maps into something else, but I can't understand Day's general framework. Can anyone help?

   In the doctine page of John’s web, it says

   Categorified Gabriel–Ulmer duality is all about recovering the syntactic doctrine from the semantic doctrine.

   It struck me that ’recovering’ is the kind of term you hear when people talk about Tannaka reconstruction theorems. Looking at the page - reconstruction theorem - I see it includes both Tannakian examples and Lawvere’s reconstruction theorem, an ancestor of Gabriel-Ulmer duality.

   So I wondered if we ever have Gabriel-Ulmer and Tannaka duality treated together, and found Brian Day in Enriched Tannaka reconstruction writing

   Our approach provides a synthesis of Tannaka reconstruction and Gabriel-Ulmer duality.

   I can see how they’re both reconstructing something by looking at the collection of maps into something else, but I can’t understand Day’s general framework. Can anyone help?

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeJul 7th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexCould you send me the Day's article ? I do not seem to have access.

   Could you send me the Day’s article ? I do not seem to have access.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 7th 2011
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexJust did so. Let me know if it doesn't arrive.

   Just did so. Let me know if it doesn’t arrive.