monoid.cppm File Reference

The Additive and Multiplicative Monoids (ℕ). More...

#include <concepts>
#include <functional>
import dedekind.category;
import dedekind.algebra:universal;

Include dependency graph for monoid.cppm:

Concepts
concept	dedekind::algebra::IsMonoid
	Proposition: a set object X whose carrier X::Domain forms a monoid — the set-indexed lift of category::IsMonoid.
concept	dedekind::algebra::IsAdditiveMonoid
	Proposition: a set object X whose carrier is a monoid under +.
concept	dedekind::algebra::IsMultiplicativeMonoid
	Proposition: a set object X whose carrier is a monoid under *.

Detailed Description

The Additive and Multiplicative Monoids (ℕ).

@partition :monoid

Copyright

2026 The Dedekind Authors Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License.

monoid__Taxonomy_of_Identity

This partition grounds the abstract categorical Monoid into the established arithmetic notation of Algebra. It reifies the "Rules of Neutrality" for Addition (0) and Multiplication (1), establishing the skeletal foundation for all higher-order Ring and Field structures.

Note

« Wprowadzenie pojęcia kategorii pozwala na jednolite traktowanie różnych struktur matematycznych. » (The introduction of the concept of a category allows for a uniform treatment of various mathematical structures.) — Samuel Eilenberg, 'Algebraic Topology'