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Is a functor which has a left adjoint and which is also its right adjoint an equivalence ?
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Is a functor which left adjoint and right adjoint an equivalence ?

I am looking for a counter-example of two functors F : C -> D and G : D->C such that

1) F is left adjoint to G

2) F is right adjoint to G

3) F is not an equivalence (ie F is not a quasi-inverse of G)