Theorems · Definition · category theory

CategoryTheory.Limits.FormalCoproduct.cochainComplexFunctor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {A : Type u'} →
      [inst_1 : CategoryTheory.Category.{v', u'} A] →
        [CategoryTheory.Limits.HasProducts A] →
          CategoryTheory.SimplicialObject (CategoryTheory.Limits.FormalCoproduct C) →
            [inst_3 : CategoryTheory.Preadditive A] →
              CategoryTheory.Functor (CategoryTheory.Functor Cᵒᵖ A) (CochainComplex A ℕ)

Given a simplicial object E in the category FormalCoproduct C, this is the functor (Cᵒᵖ ⥤ A) ⥤ CochainComplex A ℕ which sends P : Cᵒᵖ ⥤ A to the cochain complex which in degree n consists of the "evaluation" of P on E _⦋n⦌.

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.Cech

Cited by

3 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasProductsCategoryTheory.Preadditive