Theorems · Theorem · category theory

ChainComplex.map_chain_complex_of

∀ {W₁ : Type u_3} {W₂ : Type u_4} [inst : CategoryTheory.Category.{v_2, u_3} W₁]
  [inst_1 : CategoryTheory.Category.{v_3, u_4} W₂] [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁]
  [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] {α : Type u_5} [inst_4 : AddRightCancelSemigroup α]
  [inst_5 : One α] [inst_6 : DecidableEq α] (F : CategoryTheory.Functor W₁ W₂) [inst_7 : F.PreservesZeroMorphisms]
  (X : α → W₁) (d : (n : α) → X (n + 1) ⟶ X n)
  (sq : ∀ (n : α), CategoryTheory.CategoryStruct.comp (d (n + 1)) (d n) = 0),
  (F.mapHomologicalComplex (ComplexShape.down α)).obj (ChainComplex.of X d sq) =
    ChainComplex.of (fun n => F.obj (X n)) (fun n => F.map (d n)) ⋯

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsAddRightCancelSemigroupOneDecidableEqCategoryTheory.Functor.PreservesZeroMorphisms