Theorems · Theorem · category theory
prevD_eq
∀ {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} (f : (i j : ι) → C.X i ⟶ D.X j) {j j' : ι},
c.Rel j' j → (prevD j) f = CategoryTheory.CategoryStruct.comp (f j j') (D.d j' j)- Defined in
- Mathlib.Algebra.Homology.Homotopy
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · 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.dstatement · cited by 598
- ComplexShape.Relstatement and proof · cited by 518
- ComplexShape.prevproof · cited by 223
Cited by3
Results whose statement or proof uses this declaration.
- Homotopy.nullHomotopicMap_f_of_not_rel_leftproof · cited by 1
- Homotopy.nullHomotopicMap_fproof · cited by 1
- CochainComplex.HomComplex.δ_ofHomotopyproof · cited by 0