Theorems · Inductive type · category theory

CategoryTheory.Comma

{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] →
            CategoryTheory.Functor A T → CategoryTheory.Functor B T → Type (max u₁ u₂ v₃)

The objects of the comma category are triples of an object left : A, an object right : B and a morphism hom : L.obj left ⟶ R.obj right.

Defined in

Mathlib.CategoryTheory.Comma.Basic

Cited by

566 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category