Theorems · Theorem · algebraic topology
SSet.Path.arrow_src
∀ {X : SSet} {n : ℕ} (f : X.Path n) (i : Fin n),
(CategoryTheory.ConcreteCategory.hom (CategoryTheory.SimplicialObject.δ X 1)) (f.arrow i) = f.vertex i.castSuccThe source of a 1-simplex in a path is identified with the source vertex.
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- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- SimplexCategorystatement · cited by 2,204
- TypeCat.Funstatement · cited by 1,307
- SSetstatement and proof · cited by 1,283
- CategoryTheory.SimplicialObject.δstatement · cited by 188
- SSet.Pathstatement and proof · cited by 46
- SSet.Path.arrowstatement · cited by 27
- SSet.Path.vertexstatement · cited by 19
- SSet.Truncated.Path.arrow_srcproof · cited by 2
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