Theorems · Theorem · category theory

CategoryTheory.PreOneHypercover.toPullback_fst

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {S : C} (E : CategoryTheory.PreOneHypercover S) {i₁ i₂ : E.I₀}
  [inst_1 : CategoryTheory.Limits.HasPullback (E.f i₁) (E.f i₂)] (k : E.I₁ i₁ i₂),
  CategoryTheory.CategoryStruct.comp (E.toPullback k) (CategoryTheory.Limits.pullback.fst (E.f i₁) (E.f i₂)) = E.p₁ k

Defined in

Mathlib.CategoryTheory.Sites.Hypercover.One

Cited by

1 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullback