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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.

Defined in
Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic
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.

ProfiniteGrp.limit · cited by 23ProfiniteGrp.limitInfiniteGalois.proj · cited by 6InfiniteGalois.projInfiniteGalois.mulEquivToLimit · cited by 3InfiniteGalois.mulEquivTo…InfiniteGalois.toAlgEquivAux_eq_proj_of_mem · cited by 2InfiniteGalois.toAlgEquiv…ProfiniteGrp.toLimitFun · cited by 1ProfiniteGrp.toLimitFunProfiniteGrp.denseRange_toLimit · cited by 1ProfiniteGrp.denseRange_t…InfiniteGalois.algEquivToLimit · cited by 1InfiniteGalois.algEquivTo…InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj · cited by 1InfiniteGalois.finGaloisG…ProfiniteGrp.ProfiniteCompletion.denseRange · cited by 1ProfiniteCompletion.dense…ProfiniteGrp.limit_ext · cited by 1ProfiniteGrp.limit_extInfiniteGalois.isOpen_mulEquivToLimit_image_fixingSubgroup · cited by 1InfiniteGalois.isOpen_mul…InfiniteGalois.proj_adjoin_singleton_val · cited by 1InfiniteGalois.proj_adjoi…InfiniteGalois.proj_of_le · cited by 1InfiniteGalois.proj_of_leInfiniteGalois.toAlgEquivAux_eq_liftNormal · cited by 0InfiniteGalois.toAlgEquiv…ProfiniteGrp.toLimitFun_continuous · cited by 0ProfiniteGrp.toLimitFun_c…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapSet.ofPred · cited by 6101Set.ofPredSubgroup · cited by 3593SubgroupTopCat.carrier · cited by 3184TopCat.carrierTopCat · cited by 1889TopCatCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…TotallyDisconnectedSpace · cited by 295TotallyDisconnectedSpaceCompHausLike.toTop · cited by 258CompHausLike.toTopProfiniteGrp.toProfinite · cited by 51ProfiniteGrp.toProfiniteProfiniteGrp · cited by 47ProfiniteGrpProfiniteGrp.Hom.hom · cited by 20Hom.homProfiniteGrp.limitConePtAuxCITED BYCITES

Cites15

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Cited by26

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