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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 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
   • CommentTimeMay 18th 2012
   • (edited May 18th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItex[[categorical wreath product]]. Finally.

   categorical wreath product. Finally.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMay 18th 2012
   • (edited May 18th 2012)
   • PermaLink
   Author: zskoda
   Format: MarkdownItexIt looks a bit abstract. How/why the usual wreath product in group theory would come as a special or parallel case ? The wreath product in group theory has interesting generalizations in 2-category theory studied by Australian school (Street, Lack) and by them and [[Gabriella Böhm]] ([article list](http://www.rmki.kfki.hu/~bgabr)) in relation to formal theory of monads and, more recently, weak monads. Cf. the weak wreath product in * [[G. Böhm]], _On the iteration of weak wreath products_, Theory and Appl. of Categories __26__ (2012), no. 2, 30-59, [arXiv:1110.0652](http://arxiv.org/abs/1110.0652) Hopefully one could find a more formal relation to your entry...

   It looks a bit abstract. How/why the usual wreath product in group theory would come as a special or parallel case ?

   The wreath product in group theory has interesting generalizations in 2-category theory studied by Australian school (Street, Lack) and by them and Gabriella Böhm (article list) in relation to formal theory of monads and, more recently, weak monads. Cf. the weak wreath product in

   • G. Böhm, On the iteration of weak wreath products, Theory and Appl. of Categories 26 (2012), no. 2, 30-59, arXiv:1110.0652

   Hopefully one could find a more formal relation to your entry…

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 18th 2012
   • (edited May 18th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItex> It looks a bit abstract. How/why the usual wreath product in group theory would come as a special or parallel case ? In both cases the elements of the wreath product are naturally visualized as _[wreaths](http://en.wikipedia.org/wiki/Wreath)_ formed from the given elements.

   It looks a bit abstract. How/why the usual wreath product in group theory would come as a special or parallel case ?

   In both cases the elements of the wreath product are naturally visualized as wreaths formed from the given elements.

4. • CommentRowNumber4.
   • CommentAuthorzskoda
   • CommentTimeMay 18th 2012
   • PermaLink
   Author: zskoda
   Format: MarkdownItexBut are they special cases of the same construction or not ?

   But are they special cases of the same construction or not ?

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 18th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI don't think they have a non-trivial overlap, no. I briefly looked at the article by Böhm that you pointed to. (You should put that into the relevant $n$Lab entry.) But in the short time that I looked at it I could not quite relate that, either.

   I don’t think they have a non-trivial overlap, no.

   I briefly looked at the article by Böhm that you pointed to. (You should put that into the relevant $n$Lab entry.) But in the short time that I looked at it I could not quite relate that, either.