Theorems · Theorem · category theory

SimplexCategory.Truncated.morphismProperty_eq_top

∀ {d : ℕ} (W : CategoryTheory.MorphismProperty (SimplexCategory.Truncated d)) [W.IsMultiplicative],
  (∀ (n : ℕ) (hn : n < d) (i : Fin (n + 2)), W (SimplexCategory.Truncated.δ d i ⋯ ⋯)) →
    (∀ (n : ℕ) (hn : n < d) (i : Fin (n + 1)), W (SimplexCategory.Truncated.σ d i ⋯ ⋯)) → W = ⊤

Defined in: Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty
Cited by: 2 results in Mathlib
Foundations: Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.MorphismProperty.IsMultiplicative

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Cites37

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

DFunLike.coeproof · cited by 62,936
Quiver.Homproof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
Top.topstatement and proof · cited by 9,680
CategoryTheory.CategoryStruct.idproof · cited by 6,235
SimplexCategorystatement and proof · cited by 2,204
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
le_antisymmproof · cited by 2,068
CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
CategoryTheory.Monoproof · cited by 893
CategoryTheory.InducedCategory.Hom.homproof · cited by 850
CategoryTheory.Epiproof · cited by 688

Cited by2

Results whose statement or proof uses this declaration.

SSet.Truncated.liftOfStrictSegal.naturalityProperty_eq_topproof · cited by 0
SimplexCategory.morphismProperty_eq_topproof · cited by 0