Mathlib Map

Theorems · Definition · general topology

Profinite.limitCone

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] → (F : CategoryTheory.Functor J Profinite) → CategoryTheory.Limits.Cone F

An explicit limit cone for a functor F : J ⥤ Profinite, defined in terms of CompHaus.limitCone, which is defined in terms of TopCat.limitCone.

Defined in
Mathlib.Topology.Category.Profinite.Basic
Cited by
1 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.SmallCategory

Around this declaration

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

ProfiniteGrp.limitConeIsLimit · cited by 1ProfiniteGrp.limitConeIsL…ProfiniteGrp.ProfiniteCompletion.lift_eta · cited by 1ProfiniteCompletion.lift_…Profinite.isoAsLimitConeLift · cited by 0Profinite.isoAsLimitConeL…Profinite.isoindexConeLift · cited by 0Profinite.isoindexConeLiftProfiniteGrp.limitCone · cited by 0ProfiniteGrp.limitConeProfinite.limitConeIsLimit · cited by 0Profinite.limitConeIsLimitProfiniteAddGrp.limitCone · cited by 0ProfiniteAddGrp.limitConeProfinite.asLimitConeIso · cited by 0Profinite.asLimitConeIsoProfinite.asLimitindexConeIso · cited by 0Profinite.asLimitindexCon…ProfiniteAddGrp.limitConeIsLimit · cited by 0ProfiniteAddGrp.limitCone…CategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Functor.comp · cited by 6529Functor.compTopCat.carrier · cited by 3184TopCat.carrierTopCat · cited by 1889TopCatCategoryTheory.Limits.Cone.pt · cited by 1298Cone.ptCategoryTheory.InducedCategory.Hom.hom · cited by 850Hom.homCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Limits.Cone.π · cited by 500Cone.πCategoryTheory.SmallCategory · cited by 480CategoryTheory.SmallCateg…TotallyDisconnectedSpace · cited by 295TotallyDisconnectedSpaceCompHausLike.toTop · cited by 258CompHausLike.toTopProfinite · cited by 75ProfiniteCategoryTheory.InducedCategory.homMk · cited by 33InducedCategory.homMkprofiniteToCompHaus · cited by 5profiniteToCompHausProfinite.limitConeCITED BYCITES

Cites16

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Cited by10

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