Theorems · Definition · algebraic topology
SSet.Subcomplex.lift
{X Y : SSet} → (f : X ⟶ Y) → {B : Y.Subcomplex} → SSet.Subcomplex.range f ≤ B → (X ⟶ B.toSSet)Given a morphism of simplicial sets f : X ⟶ Y whose
range is ≤ B for some B : Y.Subcomplex, this is the
induced morphism X ⟶ B.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- Oppositestatement · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.Subcomplexstatement and proof · cited by 461
- SSet.Subcomplex.toSSetstatement · cited by 315
- SSet.Subcomplex.rangestatement and proof · cited by 49
- CategoryTheory.Subfunctor.liftproof · cited by 9
Cited by24
Results whose statement or proof uses this declaration.
- SSet.relativeCellComplexOfMono.bproof · cited by 12
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapToSuccproof · cited by 9
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapHornproof · cited by 8
- SSet.relativeCellComplexOfMono.tproof · cited by 7
- SSet.Subcomplex.unionProd.ι₁proof · cited by 6
- SSet.Subcomplex.unionProd.ι₂proof · cited by 6
- SSet.Subcomplex.toOfSimplexproof · cited by 6
- SSet.boundary.ιproof · cited by 5
- SSet.Subcomplex.prodIsoproof · cited by 3
- SSet.Subcomplex.toImageproof · cited by 3
- SSet.relativeCellComplexOfMono.wproof · cited by 3
- SSet.Subcomplex.fromPreimageproof · cited by 3