Theorems · Definition · category theory
dNext
{ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Preadditive V] →
{c : ComplexShape ι} → {C D : HomologicalComplex V c} → (i : ι) → ((i j : ι) → C.X i ⟶ D.X j) →+ (C.X i ⟶ D.X i)The composition of C.d i (c.next i) ≫ f (c.next i) i.
- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- AddMonoidHomstatement · cited by 3,230
- HomologicalComplex.Xstatement and proof · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.dproof · cited by 598
- ComplexShape.nextproof · cited by 297
- AddMonoidHom.mk'proof · cited by 25
Cited by23
Results whose statement or proof uses this declaration.
- Homotopy.nullHomotopicMapproof · cited by 11
- Homotopy.extproof · cited by 4
- dNext_eqstatement and proof · cited by 3
- Homotopy.commstatement · cited by 2
- Homotopy.mk.injstatement and proof · cited by 1
- Homotopy.mk.noConfusionstatement and proof · cited by 1
- Homotopy.nullHomotopicMap_f_of_not_rel_leftproof · cited by 1
- Homotopy.recOnstatement and proof · cited by 0
- CochainComplex.HomComplex.δ_ofHomotopyproof · cited by 0
- Homotopy.dNext_cochainComplexstatement · cited by 0
- Homotopy.dNext_succ_chainComplexstatement · cited by 0
- Homotopy.dNext_zero_chainComplexstatement · cited by 0