Theorems · Theorem · category theory

CategoryTheory.isPullback_initial_to_of_cofan_isVanKampen

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasInitial C] {ι : Type u_3}
  {F : CategoryTheory.Functor (CategoryTheory.Discrete ι) C} {c : CategoryTheory.Limits.Cocone F},
  CategoryTheory.IsVanKampenColimit c →
    ∀ (i j : CategoryTheory.Discrete ι),
      i ≠ j →
        CategoryTheory.IsPullback (CategoryTheory.Limits.initial.to (F.obj i))
          (CategoryTheory.Limits.initial.to (F.obj j)) (c.ι.app i) (c.ι.app j)

Defined in

Mathlib.CategoryTheory.Limits.VanKampen

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitial