added pointer to:

- Glen Bredon, Section 0.1 of:
*Introduction to compact transformation groups*, Academic Press 1972 (ISBN 9780080873596, pdf)

re #3: I have made the terminology issue more explicit at *normalizer* and in particular at the beginning of *Weyl group*.

I should think it could appear latter in the page since the generalization is not so widely adopted yet. I’ve added a brief section along those lines, which could be expanded.

]]>Shall it be defined the same way in the ncatlab wiki? Or add it as an alternative definition? I.e. more general = bettter? ]]>

Re #7, presumably to find a general construction that works in different categories.

Examples. It is easy to check that the pointed categories Gp of groups, Rg of non commutative non unitary rings and R-Lie of Lie algebras on a ring R have normalizers in this sense.

There’s quite an industry of finding commonalities between categories, e.g., exactness properties. Here, this seems to be an extension of work on protomodular categories.

]]>I remember that normalizer was defined in purely cathegorical-theory terms - i.e. not as the subset of a group, but as a category on objects.

Whats the reason for defining it this way? ]]>

I’ve run into this as well. I think searching the Internet for “Weyl group” doesn’t really turn up this meaning, so I guess it isn’t really a thing in (say) group theory; but it does seem to be standard in equivariant homotopy theory.

]]>Ah, the link was to an nLab page, but presently Adeel is reconfiguring something and for the moment the whole nLab produces *Bad Gateway* errors. A direct link is, as you will have found out already, http://www.math.uni-bonn.de/people/schwede/equivariant.pdf. For earlier references: about every article on equivariant stable homotopy theory will do, notably by Greenlees-May.

Thanks! (The link in your comment produced a Bad Gateway message, but I can probably find it.)

]]>It’s standard to use it in this generality at least in the field of equivariant homotopy theory. See e.g. page 16 of *Lectures on Equivariant Stable Homotopy Theory*, but the usage goes way back.

Is “Weyl group” really standard terminology in that generality? I’d never seen that.

]]>I have edited and rearranged just a little at *normalizer*, in order to clarify a little more.