Theorems · Definition · Lie groups
ProfiniteGrp.limitConePtAux
{J : Type v} →
[inst : CategoryTheory.SmallCategory J] →
(F : CategoryTheory.Functor J ProfiniteGrp.{max v u}) → Subgroup ((j : J) → ↑(F.obj j).toProfinite.toTop)Auxiliary construction to obtain the group structure on the limit of profinite groups.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- CategoryTheory.SmallCategory
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.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- Set.ofPredproof · cited by 6,101
- Subgroupstatement · cited by 3,593
- TopCat.carrierstatement and proof · cited by 3,184
- TopCatstatement · cited by 1,889
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- TotallyDisconnectedSpacestatement · cited by 295
- CompHausLike.toTopstatement and proof · cited by 258
Cited by26
Results whose statement or proof uses this declaration.
- ProfiniteGrp.limitproof · cited by 23
- InfiniteGalois.projstatement · cited by 6
- InfiniteGalois.mulEquivToLimitstatement · cited by 3
- InfiniteGalois.toAlgEquivAux_eq_proj_of_memstatement · cited by 2
- ProfiniteGrp.toLimitFunstatement · cited by 1
- ProfiniteGrp.denseRange_toLimitstatement and proof · cited by 1
- InfiniteGalois.algEquivToLimitstatement · cited by 1
- InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_projstatement · cited by 1
- ProfiniteGrp.ProfiniteCompletion.denseRangeproof · cited by 1
- ProfiniteGrp.limit_extstatement · cited by 1
- InfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroupstatement · cited by 1
- InfiniteGalois.proj_adjoin_singleton_valstatement · cited by 1