Theorems · Definition · algebraic topology
SSet.yonedaEquiv
{X : SSet} → {n : SimplexCategory} → (SSet.stdSimplex.obj n ⟶ X) ≃ X.obj (Opposite.op n)The canonical bijection (stdSimplex.obj n ⟶ X) ≃ X.obj (op n).
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 33 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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- CategoryTheory.uliftYonedaEquivproof · cited by 34
Cited by69
Results whose statement or proof uses this declaration.
- SSet.horn.ιproof · cited by 13
- SSet.Subcomplex.Pairing.RankFunction.Cell.mapproof · cited by 12
- SSet.relativeCellComplexOfMono.Cell.mapproof · cited by 7
- SSet.Subcomplex.toOfSimplexproof · cited by 6
- SSet.Subcomplex.range_eq_ofSimplexstatement · cited by 5
- SSet.horn.faceproof · cited by 5
- SSet.Nonsingular.mono'statement · cited by 5
- SSet.yonedaEquiv_symm_naturality_leftstatement and proof · cited by 4
- SSet.yonedaEquiv_mapstatement and proof · cited by 3
- SSet.yonedaEquiv_naturalitystatement · cited by 3
- SSet.relativeCellComplexOfMono.Cell.range_map_leproof · cited by 3
- sSetTopAdj_homEquiv_stdSimplex_zeroproof · cited by 2