dedekind::sets::Complement< T, L > Struct Template Reference

The complement as an arrow on the object \(\mathrm{Sub}(T, L)\) (Subobjects, :boundaries), \(S \mapsto \neg S\): an endomorphism, its domain and codomain the one object, presented by every set object over T in L. It is an involution by the reducer's own law \(\neg\neg A \to A\): operator~ peels the node, so ~~s is s, by type, for every presentation s; the certificate reads that law at the representative. The first arrow on sets category::IsInvolution admits: the concept quantifies over the object, not over one value type (morphism__Objects_And_Their_Presentations). More...

Public Types
using	Domain = Subobjects<T, L>
using	Codomain = Subobjects<T, L>

Public Member Functions
template<typename S> requires dedekind::category::Presents<S, Subobjects<T, L>>
constexpr auto	operator() (const S &s) const

Static Public Attributes
template<typename X>
static constexpr bool	is_involutive_v
	\(\neg\neg = \mathrm{id}\), read off the reducer at the universe: ~~𝔸 is 𝔸 by type.

Detailed Description

template<typename T, IsOckhamAlgebra L = Boole>
struct dedekind::sets::Complement< T, L >

The complement as an arrow on the object \(\mathrm{Sub}(T, L)\) (Subobjects, :boundaries), \(S \mapsto \neg S\): an endomorphism, its domain and codomain the one object, presented by every set object over T in L. It is an involution by the reducer's own law \(\neg\neg A \to A\): operator~ peels the node, so ~~s is s, by type, for every presentation s; the certificate reads that law at the representative. The first arrow on sets category::IsInvolution admits: the concept quantifies over the object, not over one value type (morphism__Objects_And_Their_Presentations).

Template Parameters

T	the carrier.
L	the logic species.

Member Data Documentation

is_involutive_v

template<typename T, IsOckhamAlgebra L = Boole>

template<typename X>

bool dedekind::sets::Complement< T, L >::is_involutive_v

staticconstexpr

Initial value:

=
      std::same_as<X, Subobjects<T, L>> &&
      std::same_as<
          std::remove_cvref_t<decltype(~~std::declval<const 𝔸<T, L>&>())>,
          𝔸<T, L>>

\(\neg\neg = \mathrm{id}\), read off the reducer at the universe: ~~𝔸 is 𝔸 by type.

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

• src/main/modules/dedekind/sets/expressions.cppm