Public Types
using	Σ_cat = Cat
using	Τ_cat = Cat
using	Domain = Cat
using	Codomain = Cat
template<typename U>
using	Shape = U

Public Member Functions
constexpr Codomain	operator() (const Domain &c) const noexcept
	Object Mapping: Id(C) = C Satisfies the IsArrow requirement for Functor Arrows.
template<typename 𝗳> requires IsArrow<std::remove_cvref_t<𝗳>> && std::same_as<typename std::remove_cvref_t<𝗳>::Domain, typename Cat::Species>
constexpr auto	operator() (𝗳 f) const
	The identity's action on arrows: the arrow itself. We loosen the constraint to accept any valid arrow of the category, satisfying the "Honest" requirement that F(f) = f.

Detailed Description

template<typename Cat>
requires IsSmallCategory<Cat>
struct dedekind::category::identity_functor< Cat >

The identity functor for any category, which simply returns the input arrow as-is. This serves as the canonical identity functor for any category, ensuring that the identity morphism is preserved without alteration.

I.e. this is presumably the only functor which is truly generic across all categories, since it doesn't rely on any specific structure of the category. Concrete IsShapedFunctor model.

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

src/main/modules/dedekind/category/functor.cppm

Public Types

Public Member Functions

Detailed Description