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ABSTRACT
A pair of adjoint functors is called a Frobenius pair of the second type if
is a left adjoint of
for some category equivalences
and
. 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 recover the result that a finitely generated projective Hopf algebra over a commutative ring is always a Frobenius extension of the second kind (cf.Citation[27], Citation[17], and prove that the integral spaces of the Hopf algebra and its dual are isomorphic.
ACKNOWLEDGMENTS
Research supported by the bilateral project “Hopf Algebras in Algebra, Topology, Geometry and Physics” of the Flemish and Romanian governments.