Theorems · Theorem · category theory

CategoryTheory.Over.prodLeftIsoPullback_hom_fst

∀ {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],
  CategoryTheory.CategoryStruct.comp (Y.prodLeftIsoPullback Z).hom (CategoryTheory.Limits.pullback.fst Y.hom Z.hom) =
    CategoryTheory.Over.Hom.left CategoryTheory.Limits.prod.fst

Defined in

Mathlib.CategoryTheory.Limits.Constructions.Over.Products

Cited by

1 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasBinaryProduct