dedekind::category::Subobject< A, Chi > Struct Template Reference

The Subobject Species S ↣ A. More...

Classes
struct	Member
	The Internal Member of the Subobject. Wraps a value from the ambient space that satisfies the classifier. More...

Public Types
using	Domain = A
using	logic_species = predicate_logic_t<Chi>
	The logic species is the characteristic morphism's own when it names one, else read off its codomain Cod<Chi> (bool ↦ Boole, Ternary ↦ Kleene, a wrapper's own logic_species), with no default. Required by :lattice::IsSubobjectLattice as a CT-vocabulary metadata typedef.
using	Codomain = Cod<Chi>
	χ: A ⟶ Ω: re-export the stored rule's own codomain Cod<Chi> (the classifier the predicate returns — bool / Ternary, or a Truth<L> wrapper such as Truth<Boole> / Truth<Kleene>). Preserving it, rather than normalising to logic_species::Ω (which would unwrap Truth<L> to bool and then break IsArrow's convertible_to<Codomain> check, since Truth<L>'s conversion to its machine_type is explicit), makes a Subobject a full IsArrow / IsCharacteristic (#850), not merely a structural callable.

Public Member Functions
constexpr A	ι (const Member &m) const
	ι: S ↣ A (The Textbook Inclusion)
constexpr auto	operator() (const A &a) const
	Subobject IS the characteristic morphism — invocation s(a) forwards to the stored χ field. Structural predicate shape (per the IsSubobject refactor in this file): callers use s(a) rather than s.χ(a), so Set and Subobject expose a uniform predicate surface.
constexpr auto	π_1 (const Member &m) const
	π₁: S ⟶ X
constexpr auto	π_2 (const Member &m) const
	π_2: S ⟶ Y

Public Attributes
Chi	χ

Detailed Description

template<typename A, typename Chi>
struct dedekind::category::Subobject< A, Chi >

The Subobject Species S ↣ A.

Represents a subset of the ambient species A, defined by the characteristic morphism χ: A ⟶ Ω.

Template Parameters

A	The Ambient (Super) Species.
Chi	The type of the characteristic morphism χ.

Member Function Documentation

π_1()

template<typename A, typename Chi>

auto dedekind::category::Subobject< A, Chi >::π_1 ( const Member & m ) const

inlineconstexpr

π₁: S ⟶ X

topoi__Pullback_Projections

These projections are only valid when the Ambient space A satisfies the IsProduct concept (X × Y).

operator()()

template<typename A, typename Chi>

auto dedekind::category::Subobject< A, Chi >::operator() ( const A & a ) const

inlineconstexpr

Subobject IS the characteristic morphism — invocation s(a) forwards to the stored χ field. Structural predicate shape (per the IsSubobject refactor in this file): callers use s(a) rather than s.χ(a), so Set and Subobject expose a uniform predicate surface.

Note

Returns a value, never a reference into the classifier (Jlt Rule 1, #1061): a large truth value is a boxed value, not a reference.

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

• src/main/modules/dedekind/category/topoi.cppm