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
   • CommentTimeDec 10th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIf "All concepts are Kan extensions," "The notion of Kan extensions subsumes all the other fundamental concepts of category theory," etc., shouldn't we expect categorical logic to have something to say about them? And, in particular, won't homotopy type theory have something to say about [[(infinity,1)-Kan extensions]]?

   If “All concepts are Kan extensions,” “The notion of Kan extensions subsumes all the other fundamental concepts of category theory,” etc., shouldn’t we expect categorical logic to have something to say about them? And, in particular, won’t homotopy type theory have something to say about (infinity,1)-Kan extensions?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 10th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexHmm, maybe if it is logical in some sense, then it's [2-logical](http://www.ncatlab.org/michaelshulman/show/2-categorical+logic).

   Hmm, maybe if it is logical in some sense, then it’s 2-logical.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeDec 10th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexYeah, that was about to be my reply. (-:

   Yeah, that was about to be my reply. (-:

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 10th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexOf couse there is Kan extension in dependent sum/product.

   Of couse there is Kan extension in dependent sum/product.