Cyclic and Archimedean morphology carriers. More...

import dedekind.morphologies:floating_point;

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Detailed Description

Cyclic and Archimedean morphology carriers.

morphologies__The_Structural_Seal

« La mathématique est l'étude des structures qui sont invariantes par certains changements de forme. La morphologie est la saisie de cette stabilité. » (Mathematics is the study of structures that are invariant under certain changes of form. Morphology is the grasping of this stability.) — René Thom, 'Stabilité structurelle et morphogénèse'

morphologies__Partitions

:archimedean — IsCyclic, IsCyclicRing, IsSimplyInfinite, IsArchimedeanField, IsDedekindCompleteField, plus the CauchyPath carrier. (Sequence-side concepts IsCauchySequence and IsConvergentSequence moved to :sequences::convergence under the textbook factoring; #719 Slice 0.) Hosts the successor / generator vocabulary notes (carrier-level member API ↔ axiomatic order::IsSuccessor; modern copula-theoretic Archimedean-generator bridge).
:cyclic — the concrete cyclic carriers Modular<N> ( \(\mathbb{Z}/N\mathbb{Z}\) as a finite cyclic ring) and CyclicRing<T,N>. Both expose the operational IsCyclic shape; Modular<N> is additionally registered with the axiomatic category::IsCyclicGroup<T, std::plus<T>>.

morphologies__Taxonomic_Intent

While :algebra defines the internal harmony of a species, :morphologies defines the valid mappings (Arrows) between distinct species and the carriers that exhibit canonical morphological structure (cyclic, Archimedean, Cauchy). It establishes the criteria for "Sameness" (Isomorphism) and "Structure Preservation" (Homomorphism) across the Dedekind universe.

See also: dedekind.category:total — the axiomatic side (IsCyclicGroup, IsAbelianGroup, IsCommutativeRing).; dedekind.algebra:field — the field-level concept counterpart.

Copyright: 2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

Note: "Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country." – David Hilbert, quoted in Mathematical Circles Revisited (1971)