Theorems · Theorem · category theory

CategoryTheory.Limits.fiberwiseColimCompEvaluationIso_inv_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] (c : C)
  (X : CategoryTheory.Functor (CategoryTheory.Grothendieck F) H),
  (CategoryTheory.Limits.fiberwiseColimCompEvaluationIso c).inv.app X =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.colimit ((CategoryTheory.Grothendieck.ι F c).comp X))

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape