三角范畴中八面体公理的几个等价命题

Several Equivalent Propositions with Respect to the Octahedral Axiom in a Triangulated Category

三角范畴是一个带有自同构(称为平移)的加法范畴,并且满足4条公理,其中的一条重要公理是八面体公理.作者结合一个自同构T定义了quasi-pushout与pushout,证明了在三角范畴中其它三条公理满足之下,quasi-pushout或pushout与八面体公理等价.

A triangulated category is an addition category with an automorphism, called the translation, and satisfies the four axioms. One of which is called the octahedral axiom and plays an important role. In this paper, the author defines, in an addition category L with an automorphism, quasi-pushouts and pushouts and proves that if L satisfies the other three axions, then L has quasi-pushouts or pushouts if and only if L satisfies the octahedral axiom, where the pushouts are similar to those in an abelian category, but the definition is depond on the automorphism. Parshall and Scott have given a definition of pushout suggested by Dlab. The proposed definition contains more information which can be used conveniently.