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In mathematics, the quotient of an abelian category A {\displaystyle {\mathcal {A}}} by a Serre subcategory B {\displaystyle {\mathcal {B}}} is the abelian category A / B {\displaystyle {\mathcal {A}}/{\mathcal {B}}} which, intuitively, is obtained from A {\displaystyle {\mathcal {A}}} by ignoring all objects from B {\displaystyle {\mathcal {B}}}. There is a canonical exact functor Q : A → A / B {\displaystyle Q\colon {\mathcal {A}}\to {\mathcal {A}}/{\mathcal {B}}} whose kernel is B {\displaystyle {\mathcal {B}}}.