On corings and comodules

Hans-Eberhard Porst

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 4, page 419-425
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Porst, Hans-Eberhard. "On corings and comodules." Archivum Mathematicum 042.4 (2006): 419-425. <http://eudml.org/doc/249817>.

@article{Porst2006,
abstract = {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.},
author = {Porst, Hans-Eberhard},
journal = {Archivum Mathematicum},
keywords = {coalgebras; comodules; locally presentable categories; coalgebras; locally presentable categories; categories of corings; categories of comodules},
language = {eng},
number = {4},
pages = {419-425},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On corings and comodules},
url = {http://eudml.org/doc/249817},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Porst, Hans-Eberhard
TI - On corings and comodules
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 4
SP - 419
EP - 425
AB - 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.
LA - eng
KW - coalgebras; comodules; locally presentable categories; coalgebras; locally presentable categories; categories of corings; categories of comodules
UR - http://eudml.org/doc/249817
ER -

References

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  1. Adámek J., Porst H.–E., On varieties and covarieties in a category, Math. Structures Comput. Sci. 13 (2003), 201–232. Zbl1041.18007MR1994641
  2. Adámek J., Rosický J., Locally Presentable and Accessible Categories, Cambridge University Press, Cambridge (1994). (1994) MR1294136
  3. Barr M., Coalgebras over a Commutative Ring, J. Algebra 32 (1974), 600–610. (1974) Zbl0305.18006MR0401881
  4. Brzezinski T., Wisbauer R., Corings and Comodules, Cambridge University Press, Cambridge (2003). Zbl1035.16030MR2012570
  5. Dascalescu S., et al., Hopf Algebras - An Introduction, Marcel Dekker, New York – Basel (2001). Zbl0962.16026MR1786197
  6. MacLane S., Categories for the working mathematician, 2nd ed., Springer, New York (1998). (1998) MR1712872
  7. Makkai M., Paré. R., Accessible categories: the foundations of categorical model theory, Contemp. Math. 104. Amer. Math. Soc., Providence (1989). (1989) Zbl0703.03042MR1031717
  8. Porst H.–E., Fundamental Constructions for Coalgebras, Corings, and Comodules, preprint (2006). Zbl1145.16025MR2383288
  9. Scheja G., Storch U., Lehrbuch der Algebra, Teil 2, Teubner, Stuttgart (1988). (1988) Zbl0638.00001MR0934019
  10. Sweedler M. E., Hopf Algebras, Benjamin, New York (1969). (1969) Zbl0203.31601MR0252485
  11. Wischnewsky M. B., On linear representations of affine groups I, Pacific J. Math. 61 (1975), 551– 572. (1975) Zbl0324.18006MR0414567

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