Theorems · Inductive type · order theory
Nucleus
(X : Type u_2) → [SemilatticeInf X] → Type u_2
A nucleus is an inflationary idempotent inf-preserving endomorphism of a semilattice.
In a frame, nuclei correspond to sublocales. See nucleusIsoSublocale.
- Defined in
- Mathlib.Order.Nucleus
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement · cited by 634
Cited by55
Results whose statement or proof uses this declaration.
- Nucleus.le_applystatement and proof · cited by 5
- Nucleus.toSublocalestatement and proof · cited by 5
- Nucleus.toInfHomstatement and proof · cited by 4
- Sublocale.toNucleusstatement · cited by 4
- Nucleus.idempotentstatement and proof · cited by 3
- Nucleus.monotonestatement and proof · cited by 3
- Nucleus.toClosureOperatorstatement and proof · cited by 3
- nucleusIsoSublocalestatement and proof · cited by 2
- Nucleus.mk.injstatement · cited by 1
- Nucleus.mk.noConfusionstatement · cited by 1
- Nucleus.coe_le_coestatement and proof · cited by 1
- Nucleus.coe_toSublocalestatement and proof · cited by 1