Theorems · Theorem · category theory

SSet.Truncated.HomotopyCategory.homToNerveMk_app_one

∀ {X : SSet.Truncated 2} {C : Type u} [inst : CategoryTheory.SmallCategory C]
  (F : CategoryTheory.Functor X.HomotopyCategory C)
  (f : X.obj (Opposite.op { obj := { len := 1 }, property := _proof_12✝ })),
  (CategoryTheory.ConcreteCategory.hom
        ((SSet.Truncated.HomotopyCategory.homToNerveMk F).app
          (Opposite.op { obj := { len := 1 }, property := _proof_12✝ })))
      f =
    CategoryTheory.ComposableArrows.mk₁ (F.map (SSet.Truncated.HomotopyCategory.homMk (SSet.Truncated.Edge.mk' f)))

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction
Cited by: 1 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory

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Cites25

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

DFunLike.coestatement · cited by 62,936
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.NatTrans.appstatement · cited by 7,406
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
SimplexCategorystatement · cited by 2,204
Quiver.Hom.opstatement · cited by 1,948
TypeCat.Funstatement · cited by 1,307
SSetstatement · cited by 1,283
CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726

Cited by1

Results whose statement or proof uses this declaration.

SSet.Truncated.HomotopyCategory.homToNerveMk_app_edgeproof · cited by 1