Theorems · Inductive type · category theory

CategoryTheory.Functor.FullyFaithful

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

Structure containing the data of inverse map (F.obj X ⟶ F.obj Y) ⟶ (X ⟶ Y) of F.map in order to express that F is a fully faithful functor.

Defined in

Mathlib.CategoryTheory.Functor.FullyFaithful

Cited by

87 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category