Theorems · Definition · algebraic topology
SSet.PtSimplex.opEquiv
{X : SSet} →
{n : ℕ} → {x : X.obj (Opposite.op { len := 0 })} → X.op.PtSimplex n (SSet.opObjEquiv.symm x) ≃ X.PtSimplex n xThe bijection between n-simplices of X.op and of X
that are constant on the boundary.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- Equiv.symmstatement and proof · cited by 3,681
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.yonedaEquivproof · cited by 55
- SSet.RelativeMorphism.mapproof · cited by 51
- SSet.PtSimplexstatement and proof · cited by 41
- SSet.opstatement and proof · cited by 33
- SSet.opObjEquivstatement and proof · cited by 26
Cited by4
Results whose statement or proof uses this declaration.
- SSet.PtSimplex.opproof · cited by 2
- SSet.PtSimplex.opEquiv_apply_mapstatement and proof · cited by 0
- SSet.PtSimplex.opEquiv_symm_apply_mapstatement and proof · cited by 0
- SSet.PtSimplex.unopproof · cited by 0