Theorems · Definition · Lie groups
ProfiniteAddGrp.ProfiniteCompletion.quotientMap
{G : AddGrpCat} →
{P : ProfiniteAddGrp.{u}} →
(f : G ⟶ AddGrpCat.of ↑P.toProfinite.toTop) →
(H : OpenNormalAddSubgroup ↑P.toProfinite.toTop) →
FiniteAddGrp.of (↑G ⧸ (ProfiniteAddGrp.ProfiniteCompletion.preimage f H).toAddSubgroup) ⟶
FiniteAddGrp.of (↑P.toProfinite.toTop ⧸ ↑H.toOpenAddSubgroup)The induced map on finite quotients coming from a morphism to P.
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- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
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
- AddSubgroupstatement · cited by 3,232
- TopCat.carrierstatement and proof · cited by 3,184
- HasQuotient.Quotientstatement · cited by 2,301
- TopCatstatement · cited by 1,889
- TotallyDisconnectedSpacestatement · cited by 295
- CompHausLike.toTopstatement and proof · cited by 258
- AddGrpCatstatement and proof · cited by 80
- AddGrpCat.carrierstatement and proof · cited by 67
- ProfiniteAddGrp.toProfinitestatement and proof · cited by 31
- ProfiniteAddGrpstatement and proof · cited by 30
- OpenAddSubgroup.toAddSubgroupstatement and proof · cited by 27
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