Theorems · Theorem · category theory

CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_map_app

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {A : Type u'} [inst_1 : CategoryTheory.Category.{v', u'} A]
  [inst_2 : CategoryTheory.Limits.HasProducts A]
  (E : CategoryTheory.SimplicialObject (CategoryTheory.Limits.FormalCoproduct C)) {X Y : CategoryTheory.Functor Cᵒᵖ A}
  (f : X ⟶ Y) (X_1 : SimplexCategory),
  ((CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor E).map f).app X_1 =
    CategoryTheory.Limits.Pi.map fun i => f.app (Opposite.op ((E.obj (Opposite.op X_1)).obj i))

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.Cech

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProducts