Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity categories, from abelian ones. Ladders also allow to tilt abelian recollements, and ladders guarantee that properties like Gorenstein projective or injective are preserved by some functors in abelian recollements. Breaking symmetry is crucial in developing this theory.

中文翻译：

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阿贝尔类别的分类阶梯

介绍了阿贝尔类别的分类阶梯，并用于解决三个一般性问题。一定高度的梯子允许构造三角分类的分类，包括源自阿贝尔分类的分类和奇异分类。梯子还允许倾斜阿贝尔联排，梯子可以确保通过阿贝尔联排中的某些函子保留Gorenstein射影或内射等属性。打破对称性对于发展这一理论至关重要。