Objective Triangle Functors in Adjoint Pairs  

作　　者：Pu Zhang Lin Zhu 

机构地区：[1]School of Mathematics, Shanghai Jiao Tong University Shanghai 200240, China

出　　处：《Algebra Colloquium》2017年第4期639-646,共8页代数集刊（英文版）

摘　　要：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 Mso 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 a^tjoint 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.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 Mso 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 a^tjoint 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.

关 键 词：adjoint pair objective triangle functor unit and counit 

分 类 号：O1[理学—数学]