Pith. sign in

REVIEW 4 cited by

Categories of hypermagmas, hypergroups, and related hyperstructures

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2304.09273 v3 pith:IRSZDYWI submitted 2023-04-18 math.CT math.COmath.GRmath.RA

So Nakamura , Manuel L. Reyes This is my paper · ORCID
classification math.CTmath.COmath.GRmath.RA
keywords hypergroupscanonicalcategoriescategoryhypermagmashyperstructuresmosaicssubcategory
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains categories with desirable features such as completeness and cocompleteness, free functors, regularity, and closed monoidal structures. We show by counterexamples that such constructions cannot be carried out within the category of canonical hypergroups. This suggests that (commutative) unital, reversible hypermagmas -- which we call mosaics -- form a worthwhile generalization of (canonical) hypergroups from the categorical perspective. Notably, mosaics contain pointed simple matroids as a subcategory, and projective geometries as a full subcategory.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Valued Mosaics

    math.CT 2026-08 conditional novelty 7.0 of 10

    Valuations are made primary in the theory of commutative mosaics, yielding a category with finite limits and coproducts, and factor nesting characterizes associativity among total product-ultrametric mosaics.

  2. Matroidal representations of low rank

    math.CO 2025-02 accept novelty 7.0 of 10

    The paper completely classifies rank-3 G-invariant matroids on a finite group G, equivalently tropical subrepresentations of the Boolean regular representation, in terms of equivalence relations on coset spaces.

  3. Hypermagmas and Colored Operads: Heads, Phases, and Theta Roles

    cs.CL 2025-07 conditional novelty 6.0 of 10

    The paper shows that syntactic heads, phases, and constraints like EPP and PIC can be expressed as a colored operad bud generating system, equivalent to a colored Merge filtering process.

  4. Semirings

    math.RA 2026-02 conditional novelty 5.0 of 10

    Rowen consolidates the pair/surpassing-relation framework that extends classical algebra (roots, matrices, linear algebra, geometry) to semirings without cancellation, adding new root-factor theorems and a map of open...

Pith tools