Theorems · Definition · algebraic topology
SSet.Edge.toTruncated
{X : SSet} → {x₀ x₁ : X.obj (Opposite.op { len := 0 })} → SSet.Edge x₀ x₁ → SSet.Truncated.Edge x₀ x₁The edge of the 2-truncation of a simplicial set X that is induced
by an edge of X.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 8,081
- SimplexCategorystatement · cited by 2,204
- SSetstatement and proof · cited by 1,283
- SimplexCategory.lenstatement · cited by 542
- SimplexCategory.Truncatedstatement · cited by 236
- SSet.Truncatedstatement · cited by 214
- SSet.Truncated.Edgestatement · cited by 81
- SSet.Edgestatement and proof · cited by 55
- SSet.truncationstatement · cited by 34
Cited by13
Results whose statement or proof uses this declaration.
- SSet.Edge.edgeproof · cited by 30
- SSet.Edge.CompStructproof · cited by 25
- SSet.Edge.mapproof · cited by 7
- CategoryTheory.nerve.functorOfNerveMapproof · cited by 4
- SSet.Edge.CompStruct.idCompproof · cited by 1
- SSet.Edge.CompStruct.compIdproof · cited by 1
- CategoryTheory.nerve.nerveFunctor₂_map_functorOfNerveMapproof · cited by 0
- SSet.Edge.toTruncated_edgestatement · cited by 0
- SSet.Edge.toTruncated_idstatement · cited by 0
- SSet.Edge.CompStruct.ofEq_simplexstatement · cited by 0
- SSet.Edge.CompStruct.ofTruncatedstatement and proof · cited by 0
- SSet.Edge.CompStruct.toTruncatedstatement · cited by 0