Theorems · Definition · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId

{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.precompose F G).obj
                        (CategoryTheory.Functor.id X) ≅
                      CategoryTheory.Functor.id (CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X)

The construction precompose respects functor identities.

Defined in

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

Cited by

7 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category