Separable functors in corings
We develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-induction functor. This construction generalizes the known adjunctions for t...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120201270X |
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| _version_ | 1832551312824205312 |
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| author | J. Gómez-Torrecillas |
| author_facet | J. Gómez-Torrecillas |
| author_sort | J. Gómez-Torrecillas |
| collection | DOAJ |
| description | We develop some basic functorial techniques for the study of the
categories of comodules over corings. In particular, we prove that
the induction functor stemming from every morphism of corings has
a left adjoint, called ad-induction functor. This construction
generalizes the known adjunctions for the categories of Doi-Hopf
modules and entwined modules. The separability of the induction
and ad-induction functors are characterized, extending earlier
results for coalgebra and ring homomorphisms, as well as for
entwining structures. |
| format | Article |
| id | doaj-art-4a9d3d5b1c1145e582b849cdf1cc5712 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4a9d3d5b1c1145e582b849cdf1cc57122025-02-03T06:01:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130420322510.1155/S016117120201270XSeparable functors in coringsJ. Gómez-Torrecillas0Departamento de Álgebra, Universidad de Granada, Granada E18071, SpainWe develop some basic functorial techniques for the study of the categories of comodules over corings. In particular, we prove that the induction functor stemming from every morphism of corings has a left adjoint, called ad-induction functor. This construction generalizes the known adjunctions for the categories of Doi-Hopf modules and entwined modules. The separability of the induction and ad-induction functors are characterized, extending earlier results for coalgebra and ring homomorphisms, as well as for entwining structures.http://dx.doi.org/10.1155/S016117120201270X |
| spellingShingle | J. Gómez-Torrecillas Separable functors in corings International Journal of Mathematics and Mathematical Sciences |
| title | Separable functors in corings |
| title_full | Separable functors in corings |
| title_fullStr | Separable functors in corings |
| title_full_unstemmed | Separable functors in corings |
| title_short | Separable functors in corings |
| title_sort | separable functors in corings |
| url | http://dx.doi.org/10.1155/S016117120201270X |
| work_keys_str_mv | AT jgomeztorrecillas separablefunctorsincorings |