Theorems · Theorem · category theory

CategoryTheory.isVanKampenColimit_of_evaluation

∀ {J : Type v'} [inst : CategoryTheory.Category.{u', v'} J] {C : Type u} [inst_1 : CategoryTheory.Category.{v, u} C]
  {D : Type u_2} [inst_2 : CategoryTheory.Category.{v_2, u_2} D] [CategoryTheory.Limits.HasPullbacks D]
  [CategoryTheory.Limits.HasColimitsOfShape J D] (F : CategoryTheory.Functor J (CategoryTheory.Functor C D))
  (c : CategoryTheory.Limits.Cocone F),
  (∀ (x : C), CategoryTheory.IsVanKampenColimit (((CategoryTheory.evaluation C D).obj x).mapCocone c)) →
    CategoryTheory.IsVanKampenColimit c

Defined in

Mathlib.CategoryTheory.Limits.VanKampen

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Limits.HasColimitsOfShape