Theorems · Definition · algebraic topology
SSet.Truncated.Edge.edge
{X : SSet.Truncated 2} →
{x₀ x₁ : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge._proof_1 })} →
SSet.Truncated.Edge x₀ x₁ → X.obj (Opposite.op { obj := { len := 1 }, property := SSet.Truncated.Edge._proof_2 })A 1-simplex
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- SimplexCategory.lenstatement · cited by 542
- SimplexCategory.Truncatedstatement · cited by 236
- SSet.Truncatedstatement and proof · cited by 214
- SSet.Truncated.Edgestatement and proof · cited by 81
Cited by37
Results whose statement or proof uses this declaration.
- SSet.Edge.edgeproof · cited by 30
- SSet.Truncated.Edge.mapproof · cited by 17
- SSet.Truncated.Edge.tensorproof · cited by 16
- SSet.Truncated.Edge.CompStruct.idCompproof · cited by 10
- SSet.Truncated.Edge.CompStruct.compIdproof · cited by 7
- SSet.Truncated.Edge.extstatement and proof · cited by 5
- SSet.Truncated.Edge.src_eqstatement · cited by 3
- SSet.Truncated.Edge.tgt_eqstatement · cited by 3
- SSet.Truncated.Edge.CompStruct.extproof · cited by 2
- SSet.Truncated.Edge.exists_of_simplexstatement · cited by 2
- SSet.Truncated.Edge.map_edgestatement and proof · cited by 2
- SSet.Truncated.HomotopyCategory.congr_arrowMk_homMkstatement and proof · cited by 1