Theorems · Theorem · Lie groups

ProfiniteGrp.comp_apply

∀ {A B C : ProfiniteGrp.{u}} (f : A ⟶ B) (g : B ⟶ C) (a : ↑A.toProfinite.toTop),
  (ProfiniteGrp.Hom.hom (CategoryTheory.CategoryStruct.comp f g)) a =
    (ProfiniteGrp.Hom.hom g) ((ProfiniteGrp.Hom.hom f) a)

Defined in: Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 22 from the axioms · uses propext, Quot.sound

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Cites12

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.CategoryStruct.compstatement · cited by 17,999
TopCat.carrierstatement and proof · cited by 3,184
TopCatstatement · cited by 1,889
TotallyDisconnectedSpacestatement · cited by 295
CompHausLike.toTopstatement and proof · cited by 258
ContinuousMonoidHomstatement · cited by 104
ProfiniteGrp.toProfinitestatement and proof · cited by 51
ProfiniteGrpstatement and proof · cited by 47
ProfiniteGrp.Hom.homstatement and proof · cited by 20
ContinuousMonoidHom.comp_toFunproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsInvariant.exists_smul_of_under_eq_of_profiniteproof · cited by 0