arXiv:2610.37944 · v1

Symmetric List Objects

首次提交 2026-10-28 04:30

版本更新 2026-10-28 04:30

雷达观测 2026-10-30 10:23

摘要

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.

作者备注：Presented at MSFP'26