Re: a coalgebras over fields question.

[Terry Bisson <bisson@canisius.edu>]

Todd Trimble <trimble1 <at> optonline.net> writes:

  >The finite-dim cocommutative
> coalgebras over k coincide with the finitely presentable objects in
> CocommCoalg_k, and the category of finite-dim cocommutative
> coalgebras is dual to the category of finite-dim commutative
> algebras/k. One concludes (a la Gabriel-Ulmer duality) that there
> is an equivalence
> 
> CocommCoalg ~ Lex(CommAlg_{fd}, Set),
> 
> where the right side is the category of left exact functors on the
> category of finite-dim commutative algebras/k.


  Hans-E. Porst <porst@math.uni-bremen.de>   pointed me to 
similar results in his recent paper
"On subcategories of the category of Hopf algebras",  Arabian
Journal of Science and Enginering, (2011), DOI 10.1007/s13369-011-0090-4 

Others recommended his article  "On corings and comodules", 
Archivum Mathematicum 42 (2006), no. 4, 419-425. 

Preprints of these are available at
http://www.math.uni-bremen.de/~porst/

I am finding these comments very helpful.  Thanks greatly, Terry Bisson


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]