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Theorems · Theorem · algebraic topology

SSet.degenerate_app_apply

∀ {X Y : SSet} {n : ℕ} {x : X.obj (Opposite.op { len := n })},
  x ∈ X.degenerate n →
    ∀ (f : X ⟶ Y), (CategoryTheory.ConcreteCategory.hom (f.app (Opposite.op { len := n }))) x ∈ Y.degenerate n
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.Degenerate
Cited by
3 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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SSet.degenerate_iff_of_isIso · cited by 2SSet.degenerate_iff_of_is…SSet.hasDimensionLT_of_epi · cited by 2SSet.hasDimensionLT_of_epiSSet.degenerate_le_preimage · cited by 1SSet.degenerate_le_preima…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.range · cited by 4705Set.rangeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opTypeCat.Fun · cited by 1307TypeCat.FunSSet · cited by 1283SSetCategoryTheory.NatTrans.naturality_apply · cited by 51NatTrans.naturality_applySSet.degenerate · cited by 29SSet.degenerateSSet.degenerate_app_applyCITED BYCITES

Cites15

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Cited by3

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