Theorems · Theorem · category theory

CategoryTheory.Limits.fiberwiseColimitLimitIso.congr_simp

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {H : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} H]
  {J : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} J] {F : CategoryTheory.Functor C CategoryTheory.Cat}
  (K : CategoryTheory.Functor J (CategoryTheory.Functor (CategoryTheory.Grothendieck F) H))
  [inst_3 : ∀ (c : C), CategoryTheory.Limits.HasColimitsOfShape (↑(F.obj c)) H]
  [inst_4 : CategoryTheory.Limits.HasLimitsOfShape J H]
  [inst_5 : ∀ (c : C), CategoryTheory.Limits.PreservesLimitsOfShape J CategoryTheory.Limits.colim],
  CategoryTheory.Limits.fiberwiseColimitLimitIso K = CategoryTheory.Limits.fiberwiseColimitLimitIso K

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShapeCategoryTheory.Limits.HasLimitsOfShapeCategoryTheory.Limits.PreservesLimitsOfShape