Theorems · Definition · Lie groups

ProfiniteGrp.limitConeIsLimit

{J : Type v} →
  [inst : CategoryTheory.SmallCategory J] →
    (F : CategoryTheory.Functor J ProfiniteGrp.{max v u}) → CategoryTheory.Limits.IsLimit (ProfiniteGrp.limitCone F)

ProfiniteGrp.limitCone is a limit cone.

Defined in: Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.SmallCategory

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites25

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

Quiver.Homproof · cited by 32,603
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement and proof · cited by 16,252
CategoryTheory.NatTrans.appproof · cited by 7,406
CategoryTheory.Functor.compproof · cited by 6,529
TopCat.carrierproof · cited by 3,184
ContinuousMapproof · cited by 2,491
CategoryTheory.Limits.Cone.ptproof · cited by 1,298
CategoryTheory.InducedCategory.Hom.homproof · cited by 850
CategoryTheory.Limits.Coneproof · cited by 710
CategoryTheory.Limits.IsLimitstatement · cited by 664
CategoryTheory.Limits.Cone.πproof · cited by 500

Cited by2

Results whose statement or proof uses this declaration.

ProfiniteGrp.ProfiniteCompletion.lift_etaproof · cited by 1
ProfiniteGrp.isLimitConeproof · cited by 0