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| Triangulated Structures Induced by Triangle Functors |
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Citation： |
Zhibing ZHAO,Xianneng DU,Yanhong BAO.Triangulated Structures Induced by Triangle Functors[J].Chinese Annals of Mathematics B,2019,40(1):55~64 |
| Page view： 1257
Net amount： 811 |
Authors： |
Zhibing ZHAO; Xianneng DU;Yanhong BAO |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11401001, 11571329), the Project of
Introducing Academic Leader of Anhui University (No.01001770) and
the Research Project of Anhui Province (No.KJ2015A101). |
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| Abstract： |
Given a triangle functor $F\colon \A \to \B$, 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 $\A/\Ker F$. |
Keywords： |
Triangulated category, Triangle functor, Half image, Verdier quotient |
Classification： |
16E30, 18A22, 16E35 |
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