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.

See also

• semi-orthogonal decomposition
• Verdier quotient?