Theorems · Definition · category theory
ComplexShape.next
{ι : Type u_1} → ComplexShape ι → ι → ιAn arbitrary choice of index j such that Rel i j, if such exists.
Returns i otherwise.
- Defined in
- Mathlib.Algebra.Homology.ComplexShape
- Cited by
- 297 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 49 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.Relproof · cited by 518
Cited by364
Results whose statement or proof uses this declaration.
- HomologicalComplex.shortComplexFunctorproof · cited by 72
- HomologicalComplex.homotopyCofiber.Xproof · cited by 59
- ComplexShape.next_eq'statement · cited by 48
- HomologicalComplex.homotopyCofiber.inrXproof · cited by 33
- HomologicalComplex.natIsoSc'statement and proof · cited by 31
- HomologicalComplex.xNextproof · cited by 28
- HomologicalComplex.homotopyCofiber.sndXproof · cited by 27
- HomologicalComplex.dFromproof · cited by 26
- HomologicalComplex.liftCyclesstatement and proof · cited by 22
- HomologicalComplex.singleObjCyclesSelfIsoproof · cited by 20
- HomologicalComplex₂.d₂proof · cited by 20
- HomologicalComplex.toCyclesproof · cited by 19
Showing the 200 most cited of 364.