Theorems · Definition · Lie groups

ProfiniteGrp.ProfiniteCompletion.preimage

{G : GrpCat} →
  {P : ProfiniteGrp.{u}} →
    (G ⟶ GrpCat.of ↑P.toProfinite.toTop) → OpenNormalSubgroup ↑P.toProfinite.toTop → FiniteIndexNormalSubgroup ↑G

The preimage of an open normal subgroup under a morphism to a profinite group.

Defined in: Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion
Cited by: 2 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Quiver.Homstatement and proof · cited by 32,603
TopCat.carrierstatement and proof · cited by 3,184
TopCatstatement · cited by 1,889
TotallyDisconnectedSpacestatement · cited by 295
CompHausLike.toTopstatement and proof · cited by 258
GrpCatstatement and proof · cited by 146
GrpCat.carrierstatement · cited by 125
ProfiniteGrp.toProfinitestatement and proof · cited by 51
GrpCat.Hom.homproof · cited by 47
ProfiniteGrpstatement and proof · cited by 47
GrpCat.ofstatement and proof · cited by 32
OpenNormalSubgroupstatement and proof · cited by 27

Cited by4

Results whose statement or proof uses this declaration.

ProfiniteGrp.ProfiniteCompletion.liftproof · cited by 3
ProfiniteGrp.ProfiniteCompletion.lift_etaproof · cited by 1
ProfiniteGrp.ProfiniteCompletion.quotientMapstatement and proof · cited by 1
ProfiniteGrp.ProfiniteCompletion.preimage_lestatement · cited by 0