On Frobenius functors (and introducing that terminology):
Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu, Doi-Hopf modules, Yetter-Drinfel’d modules and Frobenius type properties, Trans. Amer. Math. Soc. 349 (1997) 4311-4342 [1997-349-11/S0002-9947-97-02004-7, pdf]
F. Castaño Iglesias, José Gómez-Torrecillas, C. Nastasescu, Frobenius functors: applications, Comm. Alg. 27 10 (1998) 4879-4900 [doi:10.1080/00927879908826735]
Stefaan Caenepeel, E. De Groot, Gigel Militaru, Frobenius Functors of the second kind, Comm. Algebra 30 (2002) 5359-5391 [arXiv:math/0106109, doi:10.1081/AGB-120015657]
Stefaan Caenepeel, Gigel Militaru, Shenglin Zhu, Frobenius and separable functors for generalized module categories and nonlinear equations, Springer Lec. Notes in Math. 1787 (2002) [gBooks]
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