Frobenius Functors of the second kind

Details Frobenius Functors of the second kind Frobenius Functors of the second kind

2001-06-13

arxiv.org/abs/math/0106109v2

Comm. Algebra 30 (2002), 5359--5391

Mathematics

Rings and Algebras

23 pages; we have a corrected a mistake in Theorem 3.4 and Corollary 3.5

Scientific paper

A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples of Frobenius pairs of the second kind. We study Frobenius pairs of the second kind between categories of modules, comodules, and comodules over a coring. We also show that a finitely generated projective Hopf algebra over a commutative ring is always a Frobenius extension of the second kind, and prove that the integral spaces of the Hopf algebra and its dual are isomorphic.

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