三角范畴中八面体公理的几个等价刻画

Several Equivalent Characterizations of Octahedral Axiom in Triangulated Categories

在三角范畴中,与好三角同构的三角是好三角,对于预三角也得到了预三角在同构下是封闭的结论.三角范畴是一个带有自同构的加法范畴,并且满足4条公理,其中1条重要的公理是八面体公理,文章给出了三角范畴中八面体公理的几个等价刻画.

Triangulated categories were introduced by Grothendieck and Verdier.Every diagram isomorphic to a triangle is a triangle in triangulated category.It is got that every diagram isomorphic to a pre-triangle is also a pre-triangle in pre-triangulated category.Triangulated category is an additive category with an autoequivalence,and triangulated category satisfies four axioms,in which the fourth axiom is often known as the Octahedral axiom.Several equivalent characterizations of octahedral axiom in triangulated categories are got.