Theorems · Theorem · algebraic topology

SSet.const_comp

∀ {X Y Z : SSet} (y : Y.obj (Opposite.op { len := 0 })) (g : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (SSet.const y) g =
    SSet.const ((CategoryTheory.ConcreteCategory.hom (g.app (Opposite.op { len := 0 }))) y)

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

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Cites23

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 and proof · cited by 17,999
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement and proof · cited by 8,081
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
Opposite.unopproof · cited by 2,231
SimplexCategorystatement and proof · cited by 2,204
Quiver.Hom.opproof · cited by 1,948
TypeCat.Funstatement · cited by 1,307

Cited by4

Results whose statement or proof uses this declaration.

SSet.stdSimplex.toSSetObj_app_const_oneproof · cited by 1
SSet.stdSimplex.toSSetObj_app_const_zeroproof · cited by 1
SSet.stdSimplex.ι₁_whiskerLeft_toSSetObjI_μproof · cited by 1
SSet.stdSimplex.ι₀_whiskerLeft_toSSetObjI_μproof · cited by 1