The subset (⊆) order on the subobject lattice Sub(T), keyed by the logic species L. This is the injected order (Ord) under which the generic lattice-law term reducer (category:lattice_term, #865/#890) normalises set expressions: Ø is its bottom (⊥, initial), 𝔸 its top (⊤, terminal). Keying by L lets the algebra markers distinguish Boole (a Boolean subobject lattice, every law) from Kleene (Heyting / De Morgan, no complement collapse). More...

Detailed Description

template<typename L = Boole>
struct dedekind::sets::subobject_order< L >

The subset (⊆) order on the subobject lattice Sub(T), keyed by the logic species L. This is the injected order (Ord) under which the generic lattice-law term reducer (category:lattice_term, #865/#890) normalises set expressions: Ø is its bottom (⊥, initial), 𝔸 its top (⊤, terminal). Keying by L lets the algebra markers distinguish Boole (a Boolean subobject lattice, every law) from Kleene (Heyting / De Morgan, no complement collapse).

The documentation for this struct was generated from the following file:

src/main/modules/dedekind/sets/boundaries.cppm