Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-28T15:20:48.739Z Has data issue: false hasContentIssue false

Relative approximations and Maschke functors

Published online by Cambridge University Press:  17 April 2009

Bin Zhu
Affiliation:
Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, China e-mail: bzhu@math.tsinghua.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The notion of approximations relative to a functor is introduced and several characterisations of relative (dual) Maschke functors are given by using them. As an application, the injective objects in the category of comodules over a coring are described.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Auslander, M. and Reiten, I., ‘Homological finite subcategories’, in Representation Theory of Algebras and Related Topics (Kyoto, 1990), London Mathematical Society Lecture Note Series, 168 (Cambridge University Press, Cambridge, 1992), PP. 142.Google Scholar
[2]Auslander, M. and Reiten, I., ‘Applications of contravariantly finite subcategories’, Adv. Math. 86 (1991), 111152.Google Scholar
[3]Auslander, M. and Smalø, S.O., ‘Almost split seqences in subcategories’, J. Algebra. 69 (1981), 426454.CrossRefGoogle Scholar
[4]Caenepeel, S., Militaru, S. and Zhu, S., Frobenius and separable functors for generalized module categories and nonlinear equations, Lecture Note in Mathematics 1787 (Springer-Verlag, Berlin, 2002).Google Scholar
[5]Caenepeel, S. and Militaru, G., ‘Maschke functors, semisimple functors and separble functors of the second kind. Applications.’, J. Pure Appl. Algebra (to appear).Google Scholar
[6]Caenepeel, S. and Zhu, B., ‘Separable bimodules and approximations’, preprint.Google Scholar
[7]Zhu, B., ‘Contravariantly finite subcategories and adjunctions’, Algebra Colloq. 8 (2001), 307314.Google Scholar