Theorems · Theorem · category theory
HomologicalComplex.pOpcycles_opcyclesToCycles
∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {c : ComplexShape ι} (K : HomologicalComplex C c) (i j : ι)
[inst_2 : K.HasHomology i] [inst_3 : K.HasHomology j],
CategoryTheory.CategoryStruct.comp (K.pOpcycles i) (K.opcyclesToCycles i j) = K.toCycles i j- Cited by
- 2 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.Category.assocproof · cited by 6,433
- 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.dproof · cited by 598
- CategoryTheory.cancel_monoproof · cited by 435
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.cyclesstatement and proof · cited by 164
Cited by2
Results whose statement or proof uses this declaration.
- HomologicalComplex.pOpcycles_opcyclesToCycles_assocproof · cited by 2
- HomologicalComplex.HomologySequence.composableArrows₃_exactproof · cited by 0