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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 18th 2012
• (edited May 18th 2012)
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeMay 18th 2012
• (edited May 18th 2012)

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…

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 18th 2012
• (edited May 18th 2012)

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.

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeMay 18th 2012

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

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 18th 2012

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.