Triangulated Structures Induced by Triangle Functors
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摘要
Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.
Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.
Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.
引文
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[5]Ringel,C.M.and Zhang,P.,Objective tiangle functors,Sci.China Math.,58(2),2015,221-232.
[6]Ringel,C.M.and Zhang,P.,From submodule categories to preprojective algebras,Math.Z.,278(1),2014,55-73.
[7]Verider,J.L.,Des,cat′egories d′eriv′ees ab′eliennes,Asterisque,239,1996,111-125(in French).
[8]Zhang,P.,Triangulated Categories and Derived Categories,Science Press,Beijing,2015.
[2]Keller,B.,Derived categories and universal problems,Comm.Algebra,19(3),1991,699-747.
[3]Neeman,A.,Triangulated categories,Annals of Math.Studies,148,Princeton University Press,Princeton,NJ,2001.
[4]Rickard,J.,Morita theory for derived categories,J.London Math.Soc.,39(2),1989,436-456.
[5]Ringel,C.M.and Zhang,P.,Objective tiangle functors,Sci.China Math.,58(2),2015,221-232.
[6]Ringel,C.M.and Zhang,P.,From submodule categories to preprojective algebras,Math.Z.,278(1),2014,55-73.
[7]Verider,J.L.,Des,cat′egories d′eriv′ees ab′eliennes,Asterisque,239,1996,111-125(in French).
[8]Zhang,P.,Triangulated Categories and Derived Categories,Science Press,Beijing,2015.