Objective Triangle Functors in Adjoint Pairs

作     者：Pu Zhang Lin Zhu 

作者机构：School of Mathematics Shanghai Jiao Tong University Shanghai 200240 China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2017年第24卷第4期

页      面：639-646页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：国家自然科学基金 

主　　题：adjoint pair objective triangle functor unit and counit 

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.