【摘 要】
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An additive functor F:A → B between additive categories is objective if any morphism f in A with F(f) =0 factors through an object K with F(K) =0.We consider w
【机 构】
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School of Mathematics, Shanghai Jiao Tong University Shanghai 200240, China
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An additive functor F:A → B between additive categories is objective if any morphism f in A with F(f) =0 factors through an object K with F(K) =0.We consider when a triangle functor in an adjoint pair is objective.We show that a triangle functor is objective provided that its adjoint (whatever left adjoint or right adjoint) is full or dense.We also give an example to show that the adjoint of a faithful triangle functor is not necessarily objective.In particular,the adjoint of an objective triangle functor is not necessarily objective.This is in contrast to the well-known fact that the adjoint of a triangle functor is always a triangle functor.Also,for an arbitrary adjoint pair (F,G)between categories which are not necessarily additive,we give a sufficient and necessary condition such that F (resp.,G) is full or faithful.
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