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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
   • CommentTimeNov 10th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI expanded [[categorification]] a little. I had intended to point to it from a MathOverflow question, but now I feel the entry is still too underdeveloped. Hopefully we'll eventually find the time and energy to enter the big examples that drive the interest in categorification.

   I expanded categorification a little.

   I had intended to point to it from a MathOverflow question, but now I feel the entry is still too underdeveloped. Hopefully we'll eventually find the time and energy to enter the big examples that drive the interest in categorification.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • (edited Nov 11th 2009)
   • PermaLink
   Author: Urs
   Format: MarkdownI expanded [[categorification]] further: I created subsections "Variants" and started trying to describe these and how they interrelate. Currently there is now "As a section of decategorification", "As internalization in nCat", "As homtopy coherent resolution". I think this is getting now in the realm of a decent entry that does justice to this important concept, but I am still far from happy with it. More work is required.

   I expanded categorification further:

   I created subsections "Variants" and started trying to describe these and how they interrelate.

   Currently there is now "As a section of decategorification", "As internalization in nCat", "As homtopy coherent resolution".

   I think this is getting now in the realm of a decent entry that does justice to this important concept, but I am still far from happy with it. More work is required.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI added more examples to [[categorification]]. Now i felt I could link to this from <a href="http://mathoverflow.net/questions/4841/what-precisely-is-categorification">here</a>

   I added more examples to categorification.

   Now i felt I could link to this from here

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2009
   • PermaLink
   Author: Urs
   Format: MarkdownToby, you should add your MathOverflow comment on categorification to [[categorification]]. I propose we found a circle whose members vow to never ever spread any useful information without putting a copy into the nLab. If only I were better in making up good names for secret societies, I would have already done that.

   Toby,

   you should add your MathOverflow comment on categorification to categorification.

   I propose we found a circle whose members vow to never ever spread any useful information without putting a copy into the nLab. If only I were better in making up good names for secret societies, I would have already done that.