The category of finite strings
Henning Krause

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · semigroups and automata theory · DNA and Biological Computing
