Theorems · Theorem · category theory

CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId_hom_app_fst_app

∀ {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] (X_1 : CategoryTheory.Limits.CategoricalPullback.CatCommSqOver F G X)
  (X_2 : X),
  ((CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjId F G X).hom.app X_1).fst.app X_2 =
    CategoryTheory.CategoryStruct.id (X_1.fst.obj X_2)

Defined in

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

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category