Theorems · Theorem · algebraic topology

SSet.Subcomplex.image_ofSimplex

∀ {X Y : SSet} {n : ℕ} (x : X.obj (Opposite.op { len := n })) (f : X ⟶ Y),
  (SSet.Subcomplex.ofSimplex x).image f =
    SSet.Subcomplex.ofSimplex ((CategoryTheory.ConcreteCategory.hom (f.app (Opposite.op { len := n }))) x)

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Subcomplex
Cited by: 1 results in Mathlib
Foundations: Depth 65 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
Setproof · cited by 53,352
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
Oppositestatement · cited by 8,081
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
SimplexCategorystatement · cited by 2,204
le_antisymmproof · cited by 2,068
TypeCat.Funstatement · cited by 1,307
SSetstatement and proof · cited by 1,283
SSet.Subcomplexstatement · cited by 461

Cited by1

Results whose statement or proof uses this declaration.

SSet.Subcomplex.Pairing.RankFunction.Cell.image_face_index_complproof · cited by 1