Theorems · Theorem · category theory

CategoryTheory.Limits.fiberwiseColimCompColimIso_hom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {F : CategoryTheory.Functor C CategoryTheory.Cat}
  {H : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} H]
  [inst_2 : ∀ (c : C), CategoryTheory.Limits.HasColimitsOfShape (↑(F.obj c)) H]
  [inst_3 : CategoryTheory.Limits.HasColimitsOfShape C H]
  (X : CategoryTheory.Functor (CategoryTheory.Grothendieck F) H),
  CategoryTheory.Limits.fiberwiseColimCompColimIso.hom.app X = (CategoryTheory.Limits.colimitFiberwiseColimitIso X).hom

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasColimitsOfShape