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The illustration here definitely needs work. As it appears on my browser, all of the blank part of the 8 & 1/2 by 11-inch page below the diagram appears in the article, as does the page number, "1", at the bottom. Maybe I'll get to doing something about it, but if anyone out there can fix it quickly before I get to it, please do. 134.84.86.74 14:36, 14 Oct 2003 (UTC)
This definition of coalgebra is much too narrow for coalgebras as they appear in category theory and computer science. See, for instance, Jacobs and Rutten's "A Tutorial on (Co)Algebras and (Co)Induction".
Coalgebras are formally dual to algebras for a functor. It would be swell if someone included this much broader definition on this page (but I cannot volunteer today. Maybe some later day.).
These are called F-Coalgebras here. A bit strange that the more general concept is named with a longer name. -- Tillmo 10:31, 12 March 2006 (UTC)
What is a "cogebra" and where, if anywhere, has this term been used?
219.117.195.84 (
talk)
02:54, 22 May 2009 (UTC)
The word cocommutative redirects here. This article uses the word cocommutative, but doesn't define it! Someone fix this, please! John Baez ( talk) 03:35, 1 January 2010 (UTC)
Would be great if someone can include cofree coalgebras. Thanks! -- 345Kai ( talk) 18:23, 30 April 2010 (UTC)
There must be a close relationship between algebras and coalgebras, since the names are similar. Can someone knowledgeable add a clear definition that shows that relationship? For me, "reversing all arrows" doesn't work. I don't see any arrows. How about examples of tiny groups and fields, showing how to change them to cogroups and cofields? For me, that would make this clear, I think. Oh, and some motivation? What can you do with a coalgebra that you can't do just with its algebra alone? David Spector (talk) 12:26, 7 February 2012 (UTC)
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Having an informal section before the formal definition is a very good idea for this topic. However the present informal section is likely only easy if you have a rather specific set of prerequisites (quantum mechanics, representation theory), so it could do with a rewrite.
A more elementary approach could be structured along the points:
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
The illustration here definitely needs work. As it appears on my browser, all of the blank part of the 8 & 1/2 by 11-inch page below the diagram appears in the article, as does the page number, "1", at the bottom. Maybe I'll get to doing something about it, but if anyone out there can fix it quickly before I get to it, please do. 134.84.86.74 14:36, 14 Oct 2003 (UTC)
This definition of coalgebra is much too narrow for coalgebras as they appear in category theory and computer science. See, for instance, Jacobs and Rutten's "A Tutorial on (Co)Algebras and (Co)Induction".
Coalgebras are formally dual to algebras for a functor. It would be swell if someone included this much broader definition on this page (but I cannot volunteer today. Maybe some later day.).
These are called F-Coalgebras here. A bit strange that the more general concept is named with a longer name. -- Tillmo 10:31, 12 March 2006 (UTC)
What is a "cogebra" and where, if anywhere, has this term been used?
219.117.195.84 (
talk)
02:54, 22 May 2009 (UTC)
The word cocommutative redirects here. This article uses the word cocommutative, but doesn't define it! Someone fix this, please! John Baez ( talk) 03:35, 1 January 2010 (UTC)
Would be great if someone can include cofree coalgebras. Thanks! -- 345Kai ( talk) 18:23, 30 April 2010 (UTC)
There must be a close relationship between algebras and coalgebras, since the names are similar. Can someone knowledgeable add a clear definition that shows that relationship? For me, "reversing all arrows" doesn't work. I don't see any arrows. How about examples of tiny groups and fields, showing how to change them to cogroups and cofields? For me, that would make this clear, I think. Oh, and some motivation? What can you do with a coalgebra that you can't do just with its algebra alone? David Spector (talk) 12:26, 7 February 2012 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Coalgebra. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
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source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 23:22, 9 August 2017 (UTC)
Having an informal section before the formal definition is a very good idea for this topic. However the present informal section is likely only easy if you have a rather specific set of prerequisites (quantum mechanics, representation theory), so it could do with a rewrite.
A more elementary approach could be structured along the points: