Theorems · Theorem · category theory

CategoryTheory.Over.prodLeftIsoPullback_hom_fst_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C} (Y Z : CategoryTheory.Over X)
  [inst_1 : CategoryTheory.Limits.HasPullback Y.hom Z.hom] [inst_2 : CategoryTheory.Limits.HasBinaryProduct Y Z]
  {Z_1 : C} (h : Y.left ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (Y.prodLeftIsoPullback Z).hom
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst Y.hom Z.hom) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Over.Hom.left CategoryTheory.Limits.prod.fst) h

Defined in

Mathlib.CategoryTheory.Limits.Constructions.Over.Products

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasBinaryProduct