Theorems · Definition · algebraic topology
SSet.S.equivElements
{X : SSet} → X.S ≃ CategoryTheory.Functor.Elements XThe type of simplices of X : SSet.{u} identifies to the type
of elements of X considered as a functor SimplexCategoryᵒᵖ ⥤ Type u.
(Note that this is not an (anti)equivalence of categories,
see S.le_iff_nonempty_hom.)
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, 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.
- CategoryTheory.Functor.objproof · cited by 19,642
- Equivstatement · cited by 8,337
- Oppositestatement and proof · cited by 8,081
- SimplexCategorystatement and proof · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SSet.S.dimproof · cited by 162
- CategoryTheory.Functor.Elementsstatement and proof · cited by 141
- SSet.S.simplexproof · cited by 111
- SSet.Sstatement and proof · cited by 69
- Opposite.casesOnproof · cited by 37
- CategoryTheory.Functor.elementsMkproof · cited by 14
- SimplexCategory.casesOnproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- SSet.S.equivElements_apply_fststatement and proof · cited by 0
- SSet.S.equivElements_apply_sndstatement and proof · cited by 0
- SSet.S.equivElements_symm_apply_dimstatement and proof · cited by 0
- SSet.S.equivElements_symm_apply_simplexstatement and proof · cited by 0
- SSet.S.le_iff_nonempty_homstatement and proof · cited by 0