Theorems · Definition · algebraic topology
SSet.stdSimplex.asOrderHom
{n : ℕ} →
{m : SimplexCategoryᵒᵖ} → (SSet.stdSimplex.obj { len := n }).obj m → Fin ((Opposite.unop m).len + 1) →o Fin (n + 1)The m-simplices of the n-th standard simplex are
the monotone maps from Fin (m+1) to Fin (n+1).
- Cited by
- 7 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.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- 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
- OrderHomstatement · cited by 934
- SimplexCategory.lenstatement · cited by 542
- SSet.stdSimplexstatement and proof · cited by 499
- SimplexCategory.Hom.toOrderHomproof · cited by 111
Cited by9
Results whose statement or proof uses this declaration.
- SSet.hornproof · cited by 162
- SSet.boundaryproof · cited by 141
- SSet.horn_eq_iSupproof · cited by 9
- SSet.boundary_eq_iSupproof · cited by 4
- SSet.stdSimplex.coe_asOrderHom_objEquiv_symmstatement · cited by 2
- SSet.mem_horn_iffstatement · cited by 2
- SSet.boundary_zeroproof · cited by 1
- SSet.horn_objstatement · cited by 0
- SSet.objEquiv_symm_notMem_horn_of_isIsoproof · cited by 0