三角范畴的连接结构

The Adjacent Structures on Triangulated Categories

文章考虑三角范畴的连接结构.证明了若余t-结构与可裂t-结构是左连接的,则t-结构的心有足够多的投射对象.进一步地,如果三角范畴有Serre函子,则心也有足够多的内射对象.由此,说明了存在余t-结构与遗传Abel范畴的有界导出范畴上的标准t-结构左连接的充要条件是遗传Abel范畴有足够多的投射对象.若余t-结构与可裂t-结构是右连接的,则有对偶的结论.

In this paper, we consider the adjacent structure on triangulated categories. If the co-t-structure is left adjacent to a splitting t-structure, the heart of t-structure has enough projective objects. Moreover, if the triangulated category has serre functor, the heart also has enough injective objects. For this reason, there is a co-t-structure which is left adjacent to the stander t-structure on the derived category of a hereditary abelian category if and only if the hereditary abelian category has enough projective objects. The consequence is dual to the case of the right adjacent.