Theorems · Inductive type · combinatorics
PreAbstractSimplicialComplex
Type u_1 → Type u_1
An abstract simplicial complex is a collection of nonempty finite sets of points ("faces") which is downwards closed, i.e., any nonempty subset of a face is also a face.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by40
Results whose statement or proof uses this declaration.
- PreAbstractSimplicialComplex.facesstatement and proof · cited by 36
- Geometry.SimplicialComplex.toPreAbstractSimplicialComplexstatement · cited by 23
- AbstractSimplicialComplex.toPreAbstractSimplicialComplexstatement · cited by 7
- PreAbstractSimplicialComplex.isRelLowerSet_facesstatement and proof · cited by 2
- PreAbstractSimplicialComplex.mk.injstatement · cited by 1
- PreAbstractSimplicialComplex.mk.noConfusionstatement · cited by 1
- Geometry.SimplicialComplex.mk.injstatement and proof · cited by 1
- Geometry.SimplicialComplex.mk.noConfusionstatement and proof · cited by 1
- AbstractSimplicialComplex.mk.injstatement and proof · cited by 1
- AbstractSimplicialComplex.mk.noConfusionstatement and proof · cited by 1
- PreAbstractSimplicialComplex.extstatement and proof · cited by 1
- PreAbstractSimplicialComplex.recOnstatement and proof · cited by 0