magma.cppm File Reference

The Magma: base rung of the algebra tower (an algebraic set). More...

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

Include dependency graph for magma.cppm:

Concepts
concept	dedekind::algebra::IsMagma
	Proposition: a set object X whose carrier X::Domain forms a magma — the set-indexed lift of category::IsMagma.

Detailed Description

The Magma: base rung of the algebra tower (an algebraic set).

@partition :magma

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.

magma__Where_The_Two_Roads_Meet

The category tower defines the axiomatic hierarchy (category::IsMagma → IsMonoid → IsGroup → ... → IsField) at the type level, without a value constraint on the carrier. This partition opens the parallel algebra tower: the same rungs, strengthened by the universal-algebra closure tier IsAlgebra (which pins std::semiregular<T> and strict closure), so that every rung is a bona-fide algebraic set. Magma is the base; the :monoid, :group, :ring and :field partitions build the remaining rungs on the same pattern.