I want to find a functor between abelian categories, which is faithful but not full. And this functor has left and right adjoint. I want to know a nontrivial example,which is not inducecd by a ring extension. If this example can be constructed by the category of quasi-coherent sheaves,since i don't know too much about this? If someone can give me some examples?
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5$\begingroup$ Why do you want to find this? Can you give us some more context? $\endgroup$– David Roberts ♦Commented Oct 20, 2020 at 4:29
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$\begingroup$ In this paper arxiv.org/pdf/2008.11467.pdf, the author consider Frobenius functor between abelian categories. They need the functor to be faithful to make sure some counit to be epimorphsim. The examples in their paper are module categories ,the functor often restriction functor or tensor functor.So i want to know an example the category is not a module category. $\endgroup$– Sun YongLiangCommented Oct 21, 2020 at 5:31
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$\begingroup$ Thanks, that helps. $\endgroup$– David Roberts ♦Commented Oct 21, 2020 at 5:48
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