中文摘要：

主要证明如下结论：如果（C,T,Δ）是三角范畴,则C是Abelian范畴的充分且必要条件是C中三角是由同构于如下形式的态射图构成：UV〔0 0 0 1〕WV〔0 0 1 0〕T（U）W〔1 0 0 0〕T（U）T（V）.由此得到：如果C是一个Abelian范畴,T是C上的可逆加法自函子,则有且仅有一种方式使（C,T）构成三角范畴.另外,还通过Abelian范畴C上的Serre类,研究局部化范畴C[S^-1]是Abelian三角范畴的条件.

英文摘要：

Show that if（C,T,Δ） is a triangulated category,then C is an Abelian category if and only if the collection of diagramsXuYvZwT（X）in C which are isomorphic to the diagrams of the form UV〔0 0 0 1〕WV〔0 0 1 0〕T（U）W〔1 0 0 0〕T（U）T（V） are triangulations.So if C is an Abelian category and T is an additive functor which is an automorphism of the category C.Then have only a way to make（C,T） a triangulated category.Moreover also inverstigate the conditions for the localization C to be an Abelian triangulated category. Moreover also inverstigate the conditions for the localization C[S^-1] to be an Abelian triangulated category via a Serre class on the Abelian category C.