nLab admissible subcategory

A right-admissible subcategory (resp. left admissible subcategory) of a triangulated category $A$ is a strictly full triangulated subcategory $B$ such that the inclusion functor $i : B \hookrightarrow A$ admits a right adjoint $i_*$ (resp. a left adjoint $i^*$). It is called simply admissible if it is both right- and left-admissible.

Related entries

• semi-orthogonal decomposition
• Verdier quotient?

References

• Alexei Bondal, Mikhail Kapranov, Representable functors, Serre functors, and reconstructions, 53:6 (1989) 1183–1205 (in Russian, Представимые функторы, функторы Серра и пе­рестройки, Известия Академии наук СССР. Серия математическая mathnet.ru; Engl. transl. Math. USSR-Izv. 35:3 (1990) 519–541 doi)
• Stacks project, 13.40 Admissible subcategories