Theorems · Theorem · category theory

CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_extMk

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X Y : C} (R : CategoryTheory.ProjectiveResolution X) {n : ℕ}
  (f : R.complex.X n ⟶ Y) (m : ℕ) (hm : n + 1 = m) (hf : CategoryTheory.CategoryStruct.comp (R.complex.d m n) f = 0),
  R.extEquivCohomologyClass (R.extMk f m hm hf) =
    CochainComplex.HomComplex.CohomologyClass.mk
      (CochainComplex.HomComplex.Cocycle.toSingleMk
        (CategoryTheory.CategoryStruct.comp (R.cochainComplexXIso (-↑n) n ⋯).hom f) ⋯ (-↑m) ⋯ ⋯)

Defined in

Mathlib.CategoryTheory.Abelian.Projective.Ext

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt