Theorems · Definition · category theory
Profinite.indexCone
{ι : Type u} →
{X : ι → Type} →
[inst : (i : ι) → TopologicalSpace (X i)] →
{C : Set ((i : ι) → X i)} →
[inst_1 : ∀ (i : ι), T2Space (X i)] →
[inst_2 : ∀ (i : ι), TotallyDisconnectedSpace (X i)] →
(hC : IsCompact C) → CategoryTheory.Limits.Cone (Profinite.indexFunctor hC)The limit cone on indexFunctor
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Finsetstatement and proof · cited by 13,712
- Oppositestatement and proof · cited by 8,081
- Set.Elemproof · cited by 7,166
- TopCat.carrierstatement · cited by 3,184
- Opposite.unopproof · cited by 2,231
- TopCatstatement · cited by 1,889
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- CategoryTheory.Limits.Conestatement · cited by 710
- TotallyDisconnectedSpacestatement and proof · cited by 295
Cited by4
Results whose statement or proof uses this declaration.
- Profinite.NobelingProof.spanCone_isLimitproof · cited by 1
- Profinite.indexCone_isLimitstatement · cited by 0
- Profinite.asLimitindexConeIsostatement · cited by 0
- Profinite.isoindexConeLiftproof · cited by 0