Theorems · Definition · algebraic topology
SSet.stdSimplex.objEquiv
{n : SimplexCategory} → {m : SimplexCategoryᵒᵖ} → (SSet.stdSimplex.obj n).obj m ≃ (Opposite.unop m ⟶ n)Simplices of the standard simplex identify to morphisms in SimplexCategory.
- Cited by
- 59 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.
Cites9
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 and proof · cited by 8,081
- Opposite.unopstatement · cited by 2,231
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement · cited by 1,283
- SSet.stdSimplexstatement · cited by 499
- Equiv.uliftproof · cited by 115
Cited by74
Results whose statement or proof uses this declaration.
- SSet.stdSimplex.faceproof · cited by 77
- SSet.prodStdSimplex.objEquivproof · cited by 21
- SSet.horn_eq_iSupproof · cited by 9
- SSet.stdSimplex.opObjEquivproof · cited by 6
- SSet.stdSimplex.spineIdproof · cited by 6
- SSet.stdSimplex.face_singleton_complstatement · cited by 6
- SSet.stdSimplex.objMkproof · cited by 5
- SSet.stdSimplex.face_objstatement · cited by 5
- SSet.stdSimplex.nonDegenerateEquiv'proof · cited by 5
- SSet.Subcomplex.Pairing.RankFunction.Cell.type₁proof · cited by 4
- SSet.Subcomplex.Pairing.RankFunction.Cell.type₂proof · cited by 4
- SSet.boundary_eq_iSupproof · cited by 4