Theorems · Theorem · category theory

CategoryTheory.Limits.fiberwiseColim_map_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]
  {X Y : CategoryTheory.Functor (CategoryTheory.Grothendieck F) H} (α : X ⟶ Y) (c : C),
  ((CategoryTheory.Limits.fiberwiseColim F H).map α).app c =
    CategoryTheory.Limits.colim.map ((CategoryTheory.Grothendieck.ι F c).whiskerLeft α)

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasColimitsOfShape