Abstract
Separable functors were introduced by C. Năstăsescu et al. (J. Algebra 123 (1989) 397–413). We characterize separability of left or right adjoint functors defined on a Grothendieck category having a set of projective generators. This general results are particularized to the canonical functors arising from a graded homomorphism of group-graded rings (restriction of scalars, induction and coinduction functors). We relate the separability of these functors with that of their ungraded versions. In particular, we recover the characterizations given in loc. cited for the ungraded restriction of scalars and induction functors.
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