Talk:Eckmann–Hilton argument

Untitled
I made a few things a bit more understandable, hopefully. I'm no expert in algebra, so if I made any mathematical mistakes, apologies and change them. I still find the second half of the article a bit difficult to follow, to be honest. The first half is much better. Two points/questions: first, boldface is normally only used for article titles at the beginning or for emphasis of definitions, not to emphasise a phrase or sentence. Second, I'm not sure why all the magma defs need to be in quotes? I know these are usually defined for more specific structures (subcategories of Mag), but would the reader pick up the meaning from context? Revolver 00:42, 11 Mar 2004 (UTC)

a complete mess....
This article does not even state the argument concisely and neither gives a proof of it (not that it's hard). The section on the "non-monoidal case" seems overly technical. What do you think about a complete rewrite? I don't want to offend anyone, just trying to be bold: WP:BB - Saibot2 11:32, 10 March 2007 (UTC)

Visual proof
This theorem has a very nice "visual" proof, which is equivalent to the one in the article but much easier to follow (and makes the connexion to higher homotopy groups more obvious). I've written two versions of this proof. Version 2 is less ugly than version 1, but I'd like someone to de-uglify it even more before adding it to the article. Cocaineninja (talk) 18:08, 16 August 2019 (UTC)

Monoid objects in the category of monoids
The fact that monoid objects in the category of monoids are just commutative monoids is often said to be a restatement of the Eckmann-Hilton theorem, but the version of the theorem stated in this article is much more general. It implies that a unital magma object in the category of unital magmas is a commutative monoid. In fact, even this statement is less general, since it assumes that both units are equal. Cocaineninja (talk) 18:28, 16 August 2019 (UTC)