Theorems · Inductive type · category theory

CategoryTheory.Functor.Full

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

A functor F : C ⥤ D is full if for each X Y : C, F.map is surjective.

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

341 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 3 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category