Mathlib Map

Theorems · Theorem · algebraic topology

SSet.Truncated.Path.arrow_src

∀ {n : ℕ} {X : SSet.Truncated (n + 1)} {m : ℕ} (f : X.Path m) (i : Fin m),
  (CategoryTheory.ConcreteCategory.hom (X.map (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 1) ⋯ ⋯).op))
      (f.arrow i) =
    f.vertex i.castSucc

The source of a 1-simplex in a path is identified with the source vertex.

Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Path
Cited by
2 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.Truncated.Path.ext' · cited by 6Path.ext'SSet.Path.arrow_src · cited by 0Path.arrow_srcDFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opTypeCat.Fun · cited by 1307TypeCat.FunCategoryTheory.ObjectProperty.FullSubcategory · cited by 726ObjectProperty.FullSubcat…SimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSimplexCategory.δ · cited by 146SimplexCategory.δSimplexCategory.Truncated.Hom.tr · cited by 43Hom.trSSet.Truncated.Path · cited by 37Truncated.PathPath.arrow_srcCITED BYCITES

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.