Theorems · Theorem · category theory
HomologicalComplex.iCycles_d
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{ι : Type u_2} {c : ComplexShape ι} (K : HomologicalComplex C c) (i j : ι) [inst_2 : K.HasHomology i],
CategoryTheory.CategoryStruct.comp (K.iCycles i) (K.d i j) = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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.compstatement and proof · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- 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.Relproof · cited by 518
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- ComplexShape.nextproof · cited by 297
Cited by3
Results whose statement or proof uses this declaration.
- HomologicalComplex.iCycles_d_assocproof · cited by 0
- HomologicalComplex.cyclesIsKernelstatement · cited by 0
- HomologicalComplex.cycles_left_exactproof · cited by 0