Science China Mathematics

, Volume 58, Issue 2, pp 221–232 | Cite as

Objective triangle functors

Articles Progress of Projects Supported by NSFC

Abstract

An additive functor \(F:\mathcal{A} \to \mathcal{B}\) between additive categories is said to be objective, provided any morphism f in \(\mathcal{A}\) with F(f) = 0 factors through an object K with F(K) = 0. We concentrate on triangle functors between triangulated categories. The first aim of this paper is to characterize objective triangle functors F in several ways. Second, we are interested in the corresponding Verdier quotient functors \(V_F :\mathcal{A} \to \mathcal{A}/KerF\), in particular we want to know under what conditions VF is full. The third question to be considered concerns the possibility to factorize a given triangle functor F = F2F1 with F1 a full and dense triangle functor and F2 a faithful triangle functor. It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.

Keywords

triangulated category triangle functor objective functor Verdier functor 

MSC(2010)

16E30 18A22 16E35 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia

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