Triangulated Structures Induced by Triangle Functors

Abstract

Given a triangle functor F: $\mathcal{A}\rightarrow\mathcal{B}$, the authors introduce the half image hImF, which is an additive category closely related to F. If F is full or faithful, then hImF admits a natural triangulated structure. However, in general, one can not expect that hImF has a natural triangulated structure. The aim of this paper is to prove that hImF admits a natural triangulated structure if and only if F satisfies the condition (SM). If this is the case, hImF is triangle-equivalent to the Verdier quotient $\mathcal{A}$/KerF.

Keywords

Triangulated category / Triangle functor / Half image / Verdier quotient

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