The category of finite strings

TL;DR

This paper introduces the category of finite strings, explores its properties, and connects it to the augmented simplex category and linear representations, highlighting the natural emergence of non-crossing partitions.

Contribution

It defines a new categorical framework for finite strings and links it to existing mathematical structures like the augmented simplex category and non-crossing partitions.

Findings

The category of finite strings is closely related to the augmented simplex category.

Lattices of non-crossing partitions appear naturally as subobject lattices.

The framework models categories of linear representations.

Abstract

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions arises naturally as a lattice of subobjects.