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Theorems · Theorem · algebraic topology

SSet.RelativeMorphism.map_coe

∀ {X Y : SSet} {A : X.Subcomplex} {B : Y.Subcomplex} {φ : A.toSSet ⟶ B.toSSet} (f : SSet.RelativeMorphism A B φ)
  {n : SimplexCategoryᵒᵖ} (a : ↑(A.obj n)),
  (CategoryTheory.ConcreteCategory.hom (f.map.app n)) ↑a = ↑((CategoryTheory.ConcreteCategory.hom (φ.app n)) a)
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism
Cited by
1 results in Mathlib
Foundations
Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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SSet.RelativeMorphism.image_le · cited by 1RelativeMorphism.image_leDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeCategoryTheory.NatTrans.app · cited by 7406NatTrans.appSet.Elem · cited by 7166Set.ElemCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homSimplexCategory · cited by 2204SimplexCategoryTypeCat.Fun · cited by 1307TypeCat.FunSSet · cited by 1283SSetSSet.Subcomplex · cited by 461SSet.SubcomplexSSet.Subcomplex.toSSet · cited by 315Subcomplex.toSSetCategoryTheory.Subfunctor.obj · cited by 227Subfunctor.objSSet.RelativeMorphism.map · cited by 51RelativeMorphism.mapRelativeMorphism.map_coeCITED BYCITES

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