Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 42 min ago
PreprintCC BY-NC-ND 4.0arXiv

Symmetric List Objects

  • Fiona Blackett
  • Vikraman Choudhury
  • Rin Liu
Open at sourcePDFDOICite

Abstract

Cons-lists are fundamental to functional programming, and are well-understood as initial algebras, and as a concrete construction of free monoids. In category theory, such list objects can be axiomatised internal to any monoidal category, with nil and cons maps, and a recursion mechanism. When strengthened to support parametrised recursion, they can be shown to give the free monoid construction. We study a small variant on parametrised list objects called parametrised symmetric list objects, in a symmetric monoidal category, where the two frontmost elements are allowed to be permuted. We show that this gives a construction of free commutative monoids, and develop some related theory.

Related

  1. Algorithmic List Decoding of Reed-Solomon Codes up to Capacity
    Joshua Brakensiek, Yeyuan Chen, Aaron Putterman +2
    arXivPreprintCC BY 4.0Full textGeneral mathematicsarXiv
  2. List Size of Random Linear Codes: Optimality and the Limits of Average-Radius List Decoding
    Chen Yuan, Ruiqi Zhu
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  3. The List Total Colouring Conjecture is False
    Jonathan A. Noel
    arXivPreprintCC0Full textCombinatorics & discrete mathematicsarXiv
  4. The Partial List Colouring Conjecture is False
    Jonathan A. Noel
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. A polylogarithmic bound for list replicability
    Ari Blondal, Hamed Hatami, Pooya Hatami +2
    arXivPreprintCC BY-NC-SA 4.0Full textCombinatorics & discrete mathematicsStatisticsarXiv

Cite

BibTeXRIS
BibTeX
@misc{blackett2026symmetric,
  title = {{Symmetric List Objects}},
  author = {Fiona Blackett and Vikraman Choudhury and Rin Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37944},
  eprint = {2610.37944},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37944},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Symmetric List Objects
AU  - Fiona Blackett
AU  - Vikraman Choudhury
AU  - Rin Liu
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37944
UR  - https://arxiv.org/abs/2610.37944
AB  - Cons-lists are fundamental to functional programming, and are well-understood as initial algebras, and as a concrete construction of free monoids. In category theory, such list objects can be axiomatised internal to any monoidal category, with nil and cons maps, and a recursion mechanism. When strengthened to support parametrised recursion, they can be shown to give the free monoid construction. We study a small variant on parametrised list objects called parametrised symmetric list objects, in a symmetric monoidal category, where the two frontmost elements are allowed to be permuted. We show that this gives a construction of free commutative monoids, and develop some related theory.
ER  -