Theorems · Definition · category theory

CategoryTheory.Comma.mapLeft

{A : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} A] →
    {B : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
        {T : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} T] →
            (R : CategoryTheory.Functor B T) →
              {L₁ L₂ : CategoryTheory.Functor A T} →
                (L₁ ⟶ L₂) → CategoryTheory.Functor (CategoryTheory.Comma L₂ R) (CategoryTheory.Comma L₁ R)

A natural transformation L₁ ⟶ L₂ induces a functor Comma L₂ R ⥤ Comma L₁ R.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

48 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category