Theorems · Theorem · category theory

CategoryTheory.ShortComplex.opcyclesOpIso_inv_naturality_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) [inst_2 : S₁.HasLeftHomology] [inst_3 : S₂.HasLeftHomology]
  {Z : Cᵒᵖ} (h : S₁.op.opcycles ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.ShortComplex.cyclesMap φ).op
      (CategoryTheory.CategoryStruct.comp S₁.opcyclesOpIso.inv h) =
    CategoryTheory.CategoryStruct.comp S₂.opcyclesOpIso.inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.ShortComplex.opcyclesMap (CategoryTheory.ShortComplex.opMap φ)) h)

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

0 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomologyCategoryTheory.ShortComplex.HasLeftHomology