Theorems · Theorem · algebraic topology
SSet.Nonsingular.injective_map
∀ {X : SSet} [X.Nonsingular] {n : ℕ},
∀ x ∈ X.nonDegenerate n,
∀ {m : SimplexCategory} {f g : m ⟶ { len := n }},
(CategoryTheory.ConcreteCategory.hom (X.map f.op)) x = (CategoryTheory.ConcreteCategory.hom (X.map g.op)) x →
f = g- Cited by
- 1 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SSet.Nonsingular
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Equiv.symmproof · cited by 3,681
- SimplexCategorystatement and proof · cited by 2,204
- Quiver.Hom.opstatement and proof · cited by 1,948
Cited by1
Results whose statement or proof uses this declaration.
- SSet.N.existsUnique_of_leproof · cited by 2