Theorems · Definition · general topology
Profinite.limitCone
{J : Type v} →
[inst : CategoryTheory.SmallCategory J] → (F : CategoryTheory.Functor J Profinite) → CategoryTheory.Limits.Cone FAn explicit limit cone for a functor F : J ⥤ Profinite, defined in terms of
CompHaus.limitCone, which is defined in terms of TopCat.limitCone.
- 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- TopCat.carrierstatement · cited by 3,184
- TopCatstatement · cited by 1,889
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CategoryTheory.Limits.Conestatement · cited by 710
- CategoryTheory.Limits.Cone.πproof · cited by 500
- CategoryTheory.SmallCategorystatement and proof · cited by 480
- TotallyDisconnectedSpacestatement · cited by 295
- CompHausLike.toTopproof · cited by 258
Cited by10
Results whose statement or proof uses this declaration.
- ProfiniteGrp.limitConeIsLimitproof · cited by 1
- ProfiniteGrp.ProfiniteCompletion.lift_etaproof · cited by 1
- Profinite.isoAsLimitConeLiftstatement · cited by 0
- Profinite.isoindexConeLiftstatement · cited by 0
- ProfiniteGrp.limitConeproof · cited by 0
- Profinite.limitConeIsLimitstatement · cited by 0
- ProfiniteAddGrp.limitConeproof · cited by 0
- Profinite.asLimitConeIsostatement · cited by 0
- Profinite.asLimitindexConeIsostatement · cited by 0
- ProfiniteAddGrp.limitConeIsLimitproof · cited by 0