Theorems · Theorem · category theory

CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor_obj_d

∀ {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))
  [inst_3 : CategoryTheory.Preadditive A] (X : CategoryTheory.Functor Cᵒᵖ A) (i j : ℕ),
  ((CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor E).obj X).d i j =
    CochainComplex.of.d (fun n => ∏ᶜ fun i => X.obj (Opposite.op ((E.obj (Opposite.op { len := n })).obj i)))
      (AlgebraicTopology.AlternatingCofaceMapComplex.objD
        ((CategoryTheory.Limits.FormalCoproduct.cosimplicialObjectFunctor E).obj X))
      i j

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.Cech

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProductsCategoryTheory.Preadditive