Theorems · Theorem · category theory

CategoryTheory.isVanKampenColimit_extendCofan

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {n : ℕ} (f : Fin (n + 1) → C)
  {c₁ : CategoryTheory.Limits.Cofan fun i => f i.succ} {c₂ : CategoryTheory.Limits.BinaryCofan (f 0) c₁.pt},
  CategoryTheory.IsVanKampenColimit c₁ →
    CategoryTheory.IsVanKampenColimit c₂ →
      ∀ [∀ {Z : C} (i : Z ⟶ c₂.pt), CategoryTheory.Limits.HasPullback c₂.inr i]
        [CategoryTheory.Limits.HasFiniteCoproducts C],
        CategoryTheory.IsVanKampenColimit (CategoryTheory.extendCofan c₁ c₂)

Defined in

Mathlib.CategoryTheory.Limits.VanKampen

Cited by

1 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbackCategoryTheory.Limits.HasFiniteCoproducts