Dear Colleagues, let F:C -> D be a functor between two small categories. Its induced functor F^*:Fun(D,Set) -> Fun(C,Set) has both a left adjoint L and a right adjoint R. 1. Under which precise conditions on F is L F^* = Id. 2. Under which precise conditions on F is R F^* = Id. 3. Under which precise conditions on F is F^* R = Id. 4. Under which precise conditions on F is F^* L = Id. Does anybody know any answers to one of these queries? What happens if equality is replaced by natural equivalence? Does anybody know of good references to these or similar problems? Markus Pfenniger Andy Tonks School of Mathematics School of Mathematics Dean Street Dean Street Bangor, LL57 1UT Bangor, LL57 1UT UK UK ==============================================================================