A right action as a functor out of the delooping of the monoid it acts by: the one object to V, an element s to \(v \mapsto h(v, s)\). Its functor laws are the action's, \(h(v, 1) = v\) and \(h(h(v, a), b) = h(v, a \cdot b)\), which acting_monoid declares, so they are derived and not declared again. A left action registers the opposite operation, so it is a functor out of the opposite category. More...

Collaboration diagram for dedekind::category::ActionFunctor< H, V, S >:

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Public Types
using	Op = typename acting_monoid<H>::type
using	Σ_cat = Delooping<S, Op>
using	Τ_cat = ActingOn<H, V, S>
using	Domain = Σ_cat
using	Codomain = Τ_cat
template<typename U>
using	Shape = V

Public Member Functions
constexpr Codomain	operator() (const Domain &) const
constexpr Acting< H, V, S >	operator() (const Element< S, Op > &s) const
constexpr IdentityIn< Τ_cat >	operator() (const IdentityIn< Σ_cat > &) const
	The identity to the identity: the functor's unit law, at the type.

Public Attributes
H	h {}

Detailed Description

template<std::semiregular H, std::semiregular V, std::semiregular S>
requires IsRightAction<H, V, S>
struct dedekind::category::ActionFunctor< H, V, S >

A right action as a functor out of the delooping of the monoid it acts by: the one object to V, an element s to \(v \mapsto h(v, s)\). Its functor laws are the action's, \(h(v, 1) = v\) and \(h(h(v, a), b) = h(v, a \cdot b)\), which acting_monoid declares, so they are derived and not declared again. A left action registers the opposite operation, so it is a functor out of the opposite category.

Template Parameters

H	the action.
V	what it acts on.
S	the monoid's carrier.

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

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

Public Types

Public Member Functions

Public Attributes

Detailed Description