三角范畴中的函子有限子范畴

Functorially Finite Subcategories in Triangulated Categories

基于函子有限子范畴的重要性,利用图追踪的方法,从mutation对出发,得到了一类函子有限子范畴,具体而言是,设T是一个三角范畴且带有Serre函子,D是T中的一个函子有限的刚性子范畴.如果(X,Y)是一个D-mutation对,则X是T中的函子有限子范畴当且仅当Y是T中的函子有限子范畴.

Based on functorially finite subcategories, by chasing diagram, we obtain a class of functorially finite subcafegories from mutation pairs. More precisely, let T be a triangulated category with a Serre functor and D a functorially finite rigid subcategory of T. If（ X, Y） forms a D-mutation pair, then X is a functorially finite subcategory of T if and only if Y is a functorially finite subcategory of T.