Theorems · Theorem · category theory

CategoryTheory.BinaryCofan.isPullback_initial_to_of_isVanKampen

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasInitial C]
  {c : CategoryTheory.Limits.BinaryCofan X Y},
  CategoryTheory.IsVanKampenColimit c →
    CategoryTheory.IsPullback
      (CategoryTheory.Limits.initial.to
        ((CategoryTheory.Limits.pair X Y).obj { as := CategoryTheory.Limits.WalkingPair.left }))
      (CategoryTheory.Limits.initial.to
        ((CategoryTheory.Limits.pair X Y).obj { as := CategoryTheory.Limits.WalkingPair.right }))
      c.inl c.inr

Defined in

Mathlib.CategoryTheory.Limits.VanKampen

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitial