In mathematics, specifically category theory, a family of generators of a category C {\displaystyle {\mathcal {C}}} is a collection G ⊆ O b {\displaystyle {\mathcal {G}}\subseteq Ob} of objects in C {\displaystyle {\mathcal {C}}}, such that for any two distinct morphisms f, g : X → Y {\displaystyle f,g:X\to Y} in C {\displaystyle {\mathcal {C}}}, that is with f ≠ g {\displaystyle f\neq g}, there is some G {\displaystyle G} in G {\displaystyle {\mathcal {G}}} and some morphism h : G → X {\displaystyle h:G\to X} such that f ∘ h ≠ g ∘ h. Wikipedia