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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 nlab noncommutative noncommutative-geometry number-theory object 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
   • CommentTimeFeb 2nd 2011
   • (edited Feb 2nd 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI notice that the entry [[essential image]] is in a bad state: it starts out making two statements, the first of which is then doubted by Mike in a query box, the second doubted by Zoran in a query box. If there is really no agreement on what should go there, we should maybe better clear the entry, and discuss the matter here until we have a minimum of consensus. But I guess the problems can easily be dealt with and somebody should try to polish this entry right away.

   I notice that the entry essential image is in a bad state:

   it starts out making two statements, the first of which is then doubted by Mike in a query box, the second doubted by Zoran in a query box.

   If there is really no agreement on what should go there, we should maybe better clear the entry, and discuss the matter here until we have a minimum of consensus.

   But I guess the problems can easily be dealt with and somebody should try to polish this entry right away.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeFeb 2nd 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexAs far as my complaint, Toby answered to it, my memory is that I was happy with his remark at the time. So, if he puts it his way with the subtlety discussed I am happy with move of the second box to here after that (with backlink). As far as Mike's comment, I was at the time pretty sure that the definition worked very well in the world of strict n-categories at least and did not quite understand the pseudomonicity complaint. That part is not resolved as far as I am concerned.

   As far as my complaint, Toby answered to it, my memory is that I was happy with his remark at the time. So, if he puts it his way with the subtlety discussed I am happy with move of the second box to here after that (with backlink). As far as Mike’s comment, I was at the time pretty sure that the definition worked very well in the world of strict n-categories at least and did not quite understand the pseudomonicity complaint. That part is not resolved as far as I am concerned.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeFeb 4th 2011
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexYou are right, I think; pseudomonicity is only required if you want the essential image to be *equivalent* to the strict image. I've updated [[replete subcategory]] and [[essential image]] along these lines. I'm curious, though, whether there is any use for non-full essential images as defined on that page?

   You are right, I think; pseudomonicity is only required if you want the essential image to be equivalent to the strict image. I’ve updated replete subcategory and essential image along these lines. I’m curious, though, whether there is any use for non-full essential images as defined on that page?

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 4th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for taking the time to brush up that entry!

   Thanks for taking the time to brush up that entry!