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ProfiniteGrp.ProfiniteCompletion.lift_eta

∀ {G : GrpCat} {P : ProfiniteGrp.{u}} (f : G ⟶ GrpCat.of ↑P.toProfinite.toTop),
  CategoryTheory.CategoryStruct.comp (ProfiniteGrp.ProfiniteCompletion.eta G)
      ((CategoryTheory.forget₂ ProfiniteGrp.{u} GrpCat).map (ProfiniteGrp.ProfiniteCompletion.lift f)) =
    f
Defined in
Mathlib.Topology.Algebra.Category.ProfiniteGrp.Completion
Cited by
1 results in Mathlib
Foundations
Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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ProfiniteGrp.ProfiniteCompletion.lift_eta_assoc · cited by 0ProfiniteCompletion.lift_…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Iso · cited by 3963CategoryTheory.IsoMonoidHom · cited by 3629MonoidHomTopCat.carrier · cited by 3184TopCat.carrierTopCat · cited by 1889TopCatCategoryTheory.Limits.Cone.pt · cited by 1298Cone.ptCategoryTheory.Functor.const · cited by 1264Functor.constProfiniteCompletion.lift_etaCITED BYCITES

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