Theorems · Definition · category theory
ComplexShape.Embedding.BoundaryGE
{ι : Type u_1} → {ι' : Type u_2} → {c : ComplexShape ι} → {c' : ComplexShape ι'} → c.Embedding c' → ι → PropThe lower boundary of an embedding e : Embedding c c', as a predicate on ι.
It is satisfied by j : ι when there exists i' : ι' not in the image of e.f
such that c'.Rel i' (e.f j).
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- ComplexShape.Embeddingstatement and proof · cited by 337
- ComplexShape.Embedding.fproof · cited by 251
- ComplexShape.prevproof · cited by 223
Cited by57
Results whose statement or proof uses this declaration.
- HomologicalComplex.truncGE'XIsostatement and proof · cited by 14
- HomologicalComplex.truncGE'XIsoOpcyclesstatement and proof · cited by 14
- ComplexShape.Embedding.HasLiftproof · cited by 13
- HomologicalComplex.truncGE'Mapproof · cited by 12
- HomologicalComplex.truncGE'.Xproof · cited by 7
- ComplexShape.Embedding.not_boundaryGE_nextstatement · cited by 7
- HomologicalComplex.restrictionToTruncGE'.fproof · cited by 4
- HomologicalComplex.truncGE'.XIsostatement and proof · cited by 4
- HomologicalComplex.truncGE'Map_f_eqstatement and proof · cited by 4
- HomologicalComplex.truncGE'Map_f_eq_opcyclesMapstatement and proof · cited by 4
- HomologicalComplex.isIso_restrictionToTruncGE'statement and proof · cited by 4
- HomologicalComplex.restrictionToTruncGE'_naturalityproof · cited by 3