Theorems · Theorem · algebraic topology

SSet.relativeCellComplexOfMono.range_r_app_union_range_b_app

∀ {X Y : SSet} (i : X ⟶ Y) (d : ℕ) (n : SimplexCategoryᵒᵖ),
  Set.range ⇑(CategoryTheory.ConcreteCategory.hom ((SSet.relativeCellComplexOfMono.r i d).app n)) ∪
      Set.range ⇑(CategoryTheory.ConcreteCategory.hom ((SSet.relativeCellComplexOfMono.b i d).app n)) =
    Set.univ

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Skeleton
Cited by: 1 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

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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 · cited by 19,642
Oppositestatement and proof · cited by 8,081
CategoryTheory.NatTrans.appstatement · cited by 7,406
Set.rangestatement · cited by 4,705
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
Set.univstatement · cited by 3,945
SimplexCategorystatement and proof · cited by 2,204
TypeCat.Funstatement · cited by 1,307
SSetstatement and proof · cited by 1,283

Cited by1

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SSet.relativeCellComplexOfMono.isPushoutproof · cited by 0