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Theorems · Theorem · algebraic topology

SimplexCategory.toTopHomeo_symm_naturality

∀ {n m : SimplexCategory} (f : n ⟶ m),
  ⇑m.toTopHomeo.symm ∘ stdSimplex.map ⇑(CategoryTheory.ConcreteCategory.hom f) =
    ⇑(TopCat.Hom.hom (SSet.toTop.map (SSet.stdSimplex.map f))) ∘ ⇑n.toTopHomeo.symm
Defined in
Mathlib.AlgebraicTopology.SimplicialSet.TopAdj
Cited by
1 results in Mathlib
Foundations
Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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SimplexCategory.toTopHomeo_symm_naturality_apply · cited by 0SimplexCategory.toTopHome…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetQuiver.Hom · cited by 32603Quiver.HomReal · cited by 25697RealCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeSet.Elem · cited by 7166Set.ElemCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierContinuousMap · cited by 2491ContinuousMapSimplexCategory · cited by 2204SimplexCategoryTopCat · cited by 1889TopCatSSet · cited by 1283SSetSimplexCategory.toTopHomeo_sy…CITED BYCITES

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