Theorems · Definition · category theory

CategoryTheory.Limits.CategoricalPullback.functorEquiv

{A : Type u₁} →
  {B : Type u₂} →
    {C : Type u₃} →
      [inst : CategoryTheory.Category.{v₁, u₁} A] →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} B] →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} C] →
            (F : CategoryTheory.Functor A B) →
              (G : CategoryTheory.Functor C B) →
                (X : Type u₄) →
                  [inst_3 : CategoryTheory.Category.{v₄, u₄} X] →
                    CategoryTheory.Functor X (CategoryTheory.Limits.CategoricalPullback F G) ≌
                      CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X

The universal property of categorical pullbacks, stated as an equivalence of categories between functors X ⥤ (F ⊡ G) and categorical commutative squares over X.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic

Cited by

25 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category