Theorems · Theorem · algebraic topology

SSet.unique_nonDegenerate_map

∀ (X : SSet) {n : ℕ} (x : X.obj (Opposite.op { len := n })) {m : ℕ} (f₁ : { len := n } ⟶ { len := m })
  [CategoryTheory.Epi f₁] (y₁ : ↑(X.nonDegenerate m)),
  x = (CategoryTheory.ConcreteCategory.hom (X.map f₁.op)) ↑y₁ →
    ∀ (f₂ : { len := n } ⟶ { len := m }) (y₂ : ↑(X.nonDegenerate m)),
      x = (CategoryTheory.ConcreteCategory.hom (X.map f₂.op)) ↑y₂ → f₁ = f₂

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Degenerate

Cited by

3 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Epi