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Theorems · Theorem · general topology

LightProfinite.lightToProfinite_map_proj_eq

∀ (S : LightProfinite) (n : ℕ),
  lightToProfinite.map (S.proj n) =
    (lightToProfinite.obj S).asLimitCone.π.app
      ((CategoryTheory.Limits.IsCofiltered.sequentialFunctor (DiscreteQuotient ↑(lightToProfinite.obj S).toTop)).obj
        (Opposite.op n))
Defined in
Mathlib.Topology.Category.LightProfinite.AsLimit
Cited by
1 results in Mathlib
Foundations
Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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LightProfinite.proj_surjective · cited by 2LightProfinite.proj_surje…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.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.Functor.const · cited by 1264Functor.constSecondCountableTopology · cited by 750SecondCountableTopologyCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Limits.IsLimit · cited by 664Limits.IsLimitCategoryTheory.Limits.Cone.π · cited by 500Cone.πLightProfinite.lightToProfini…CITED BYCITES

Cites31

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