Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
coalgebras; comodules; locally presentable categories
coalgebras; comodules; locally presentable categories
Summary:
It is shown that the categories of $R$-coalgebras for a commutative unital ring $R$ and the category of $A$-corings for some $R$-algebra $A$ as well as their respective categories of comodules are locally presentable.
References:
[1] Adámek J., Porst H.–E.: On varieties and covarieties in a category. Math. Structures Comput. Sci. 13 (2003), 201–232. MR 1994641 | Zbl 1041.18007
[2] Adámek J., Rosický J.: Locally Presentable and Accessible Categories. Cambridge University Press, Cambridge (1994). MR 1294136
[3] Barr M.: Coalgebras over a Commutative Ring. J. Algebra 32 (1974), 600–610. MR 0401881 | Zbl 0305.18006
[4] Brzezinski T., Wisbauer R.: Corings and Comodules. Cambridge University Press, Cambridge (2003). MR 2012570 | Zbl 1035.16030
[5] Dascalescu S., et al.: Hopf Algebras - An Introduction. Marcel Dekker, New York – Basel (2001). MR 1786197 | Zbl 0962.16026
[6] MacLane S.: Categories for the working mathematician. 2nd ed., Springer, New York (1998). MR 1712872
[7] Makkai M., Paré. R.: Accessible categories: the foundations of categorical model theory. Contemp. Math. 104. Amer. Math. Soc., Providence (1989). MR 1031717 | Zbl 0703.03042
[8] Porst H.–E.: Fundamental Constructions for Coalgebras, Corings, and Comodules. preprint (2006). MR 2383288 | Zbl 1145.16025
[9] Scheja G., Storch U.: Lehrbuch der Algebra. Teil 2, Teubner, Stuttgart (1988). MR 0934019 | Zbl 0638.00001
[10] Sweedler M. E.: Hopf Algebras. Benjamin, New York (1969). MR 0252485 | Zbl 0203.31601
[11] Wischnewsky M. B.: On linear representations of affine groups I. Pacific J. Math. 61 (1975), 551– 572. MR 0414567 | Zbl 0324.18006
Search
Partner of
