Theorems · Inductive type · category theory

CategoryTheory.Functor.EssSurj

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → CategoryTheory.Functor C D → Prop

A functor F : C ⥤ D is essentially surjective if every object of D is in the essential image of F. In other words, for every Y : D, there is some X : C with F.obj X ≅ Y.

Defined in

Mathlib.CategoryTheory.EssentialImage

Cited by

88 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category