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Theorems · Theorem · algebraic topology

SSet.Truncated.Edge.map_id

∀ {X Y : SSet.Truncated 2} (x : X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge._proof_1 }))
  (f : X ⟶ Y),
  (SSet.Truncated.Edge.id x).map f =
    SSet.Truncated.Edge.id
      ((CategoryTheory.ConcreteCategory.hom
          (f.app (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Edge._proof_1 })))
        x)
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated
Cited by
1 results in Mathlib
Foundations
Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SSet.Edge.map_id · cited by 0Edge.map_idDFunLike.coe · cited by 62936DFunLike.coeQuiver.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.appCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryQuiver.Hom.op · cited by 1948Hom.opTypeCat.Fun · cited by 1307TypeCat.FunSimplexCategory.len · cited by 542SimplexCategory.lenSimplexCategory.Truncated · cited by 236SimplexCategory.TruncatedSSet.Truncated · cited by 214SSet.TruncatedSSet.Truncated.Edge · cited by 81Truncated.EdgeCategoryTheory.NatTrans.naturality_apply · cited by 51NatTrans.naturality_applyEdge.map_idCITED BYCITES

Cites21

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Cited by1

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