Theorems · Theorem · category theory
Homotopy.dNext_cochainComplex
∀ {V : Type u} [inst : CategoryTheory.Category.{v, u} V] [inst_1 : CategoryTheory.Preadditive V]
{P Q : CochainComplex V ℕ} (f : (i j : ℕ) → P.X i ⟶ Q.X j) (j : ℕ),
(dNext j) f = CategoryTheory.CategoryStruct.comp (P.d j (j + 1)) (f (j + 1) j)- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Limits.HasZeroMorphismsproof · cited by 3,275
- AddMonoidHomstatement · cited by 3,230
- HomologicalComplex.Xstatement and proof · cited by 1,839
- HomologicalComplexproof · cited by 1,691
- ComplexShapeproof · cited by 1,684
- ComplexShape.upstatement and proof · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
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