Theorems · Inductive type · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom

{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.Limits.CategoricalPullback.CatCommSqOver F G X →
                      CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X → Type (max (max u₄ v₁) v₃)

The Hom types for the categorical commutative squares over X are given by pairs of natural transformations compatible with the structural isomorphisms.

Defined in

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

Cited by

10 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category