Talk:Centralizer and normalizer

Centralizers in symmetric monoidal closed categories
If M is a monoid in a symmetric monoidal closed category V with equalizers and $$f\colon X \to M$$ is any morphism in V with codomain M, one can define the centralizer of f as the equalizer of the two multiplication maps $$M \to [X, M]$$ induced by f. GeoffreyT2000 (talk) 16:39, 17 May 2015 (UTC)

Sentence in introduction
In the beginning, it says The centralizer and normalizer of S are subgroups of G, and can provide insight into the structure of G. Can this be made more specific? In which way do they provide insight into the structure of G? Is there a particular theorem indicating this? Zaunlen (talk) 15:14, 10 November 2019 (UTC)