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arXiv · 1405.1927

Objective triangle functors

Claus Michael Ringel·Pu Zhang
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Abstract

An (additive) functor F from an additive category A to an additive category B is said to be objective, provided any morphism f in A with F(f) = 0 factors through an object K with F(K) = 0. In this paper 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, in particular we want do know under what conditions V_F is full. The third question to be considered concerns the possibility to factorize a given triangle functor F = F_2F_1 with F_1 a full and dense triangle functor and F_2 a faithful triangle functor. It turns our that the behaviour of splitting monomorphisms (and splitting epimorphisms) plays a decisive role.

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Claus Michael Ringel, Pu Zhang. 2014-05-08. Objective triangle functors. https://doi.org/10.1007/s11425-014-4954-4

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