Theorems · Theorem · category theory

CategoryTheory.DifferentialObject.d_squared_apply

∀ {β : Type u_1} [inst : AddCommGroup β] {b : β} {V : Type u_2} [inst_1 : CategoryTheory.Category.{v_1, u_2} V]
  [inst_2 : CategoryTheory.Limits.HasZeroMorphisms V]
  (X : CategoryTheory.DifferentialObject ℤ (CategoryTheory.GradedObjectWithShift b V)) {x : β},
  CategoryTheory.CategoryStruct.comp (X.d x) (X.d ((fun b_1 => b_1 + { as := 1 }.as • b) x)) = 0

Defined in

Mathlib.Algebra.Homology.DifferentialObject

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms