![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Is it really correct to call the simple construction (of the universal covering group of a monoid) the Grothendieck group? Every time I've seen it presented, it was done so without the Grothendieck name attached to it, whereas the Grothendiek group is only discussed for Abelian categories, and not just on plain monoids (which is more simply the "universal abelian group" or something like that. linas 19:36, 1 April 2007 (UTC)
It seems pretty obvious that cancellation is necessary for this construction. So why is there no mention of it? Thehotelambush ( talk) 22:43, 30 September 2008 (UTC)
Never mind, the +k accounts for this. Thehotelambush ( talk) 04:27, 9 May 2009 (UTC)
-- Bart.karviainen ( talk) 13:14, 25 May 2010 (UTC)
The first sentence of the article is vague and not rigorous. It says: "the grothendieck construction...constructs an abelian group from a commutative monoid, in the best possible way". It is definitely unclear what "best" means in this case. -- Bart.karviainen ( talk) 13:34, 25 May 2010 (UTC)
There is a clarify-tag for "zero element", and perhaps it is time to clarify it. Commutative monoid operation is quite often denoted by +, and accordingly, its neutral element by 0, which is what most people would instantly think of as "the zero element". Would "absorbing element" be less confusing, and much less unmotivating, or am I missing something? Lapasotka ( talk) 13:15, 6 May 2022 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
Is it really correct to call the simple construction (of the universal covering group of a monoid) the Grothendieck group? Every time I've seen it presented, it was done so without the Grothendieck name attached to it, whereas the Grothendiek group is only discussed for Abelian categories, and not just on plain monoids (which is more simply the "universal abelian group" or something like that. linas 19:36, 1 April 2007 (UTC)
It seems pretty obvious that cancellation is necessary for this construction. So why is there no mention of it? Thehotelambush ( talk) 22:43, 30 September 2008 (UTC)
Never mind, the +k accounts for this. Thehotelambush ( talk) 04:27, 9 May 2009 (UTC)
-- Bart.karviainen ( talk) 13:14, 25 May 2010 (UTC)
The first sentence of the article is vague and not rigorous. It says: "the grothendieck construction...constructs an abelian group from a commutative monoid, in the best possible way". It is definitely unclear what "best" means in this case. -- Bart.karviainen ( talk) 13:34, 25 May 2010 (UTC)
There is a clarify-tag for "zero element", and perhaps it is time to clarify it. Commutative monoid operation is quite often denoted by +, and accordingly, its neutral element by 0, which is what most people would instantly think of as "the zero element". Would "absorbing element" be less confusing, and much less unmotivating, or am I missing something? Lapasotka ( talk) 13:15, 6 May 2022 (UTC)