Theorems · Theorem · category theory

CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor_obj_map

∀ {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 : CategoryTheory.Functor Cᵒᵖ A)
  {X_1 Y : SimplexCategory} (f : X_1 ⟶ Y),
  ((CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor E).obj X).map f =
    CategoryTheory.Limits.Pi.lift fun i =>
      CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.Pi.π (fun i => X.obj (Opposite.op ((E.obj (Opposite.op X_1)).obj i))) ((E.map f.op).f i))
        (X.map ((E.map f.op).φ i).op)

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