Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcycles_exact

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] [inst_2 : CategoryTheory.Abelian C]
  (X : CategoryTheory.Abelian.SpectralObject C ι) {i j k : ι} (f : i ⟶ j) (g : j ⟶ k) (fg : i ⟶ k)
  (h : CategoryTheory.CategoryStruct.comp f g = fg) (n : ℤ), (X.kernelSequenceOpcycles f g fg h n).Exact

opZ^n(f, g) identifies to the kernel of H^n(f ≫ g) ⟶ H^n(g).

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian