Theorems · Theorem · category theory

HomologicalComplex.fromOpcycles_op_cyclesOpIso_inv_assoc

∀ {ι : Type u_1} {V : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} V] {c : ComplexShape ι}
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] (K : HomologicalComplex V c) (i : ι) [inst_2 : K.HasHomology i]
  (j : ι) {Z : Vᵒᵖ} (h : K.op.cycles i ⟶ Z),
  CategoryTheory.CategoryStruct.comp (K.fromOpcycles i j).op
      (CategoryTheory.CategoryStruct.comp (K.cyclesOpIso i).inv h) =
    CategoryTheory.CategoryStruct.comp (K.op.toCycles j i) h

Defined in

Mathlib.Algebra.Homology.Opposite

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology