Theorems · Theorem · algebraic topology

SSet.yonedaEquiv_symm_naturality_left

∀ {X : SSet} {m n : SimplexCategory} (f : m ⟶ n) (g : X.obj (Opposite.op n)),
  CategoryTheory.CategoryStruct.comp (SSet.stdSimplex.map f) (SSet.yonedaEquiv.symm g) =
    SSet.yonedaEquiv.symm ((CategoryTheory.ConcreteCategory.hom (X.map f.op)) g)

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex
Cited by: 4 results in Mathlib
Foundations: Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites18

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
Equivstatement · cited by 8,337
Oppositestatement · cited by 8,081
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
Equiv.symmstatement and proof · cited by 3,681
SimplexCategorystatement and proof · cited by 2,204
Quiver.Hom.opstatement and proof · cited by 1,948
TypeCat.Funstatement · cited by 1,307

Cited by4

Results whose statement or proof uses this declaration.

SSet.N.stdSimplex_map_monoOfLE_yonedaEquiv_symm_simplexproof · cited by 1
SSet.stdSimplex.δ_comp_yonedaEquiv_symmproof · cited by 0
SSet.yonedaEquiv_symm_naturality_left_assocproof · cited by 0
SSet.stdSimplex.σ_comp_yonedaEquiv_symmproof · cited by 0