Calculations for Plus Constructions

TL;DR

This paper explores various methods for constructing unique factorization categories (UFCs) and demonstrates how the plus construction can reproduce and clarify many existing constructions through explicit computations.

Contribution

It introduces new methods for constructing UFCs and shows how the plus construction unifies and clarifies existing approaches with explicit examples.

Findings

Plus construction reproduces known UFCs

Explicit computations clarify the plus construction

New methods for UFC construction are presented

Abstract

In arXiv:2209.06121, they defined a general plus construction for monoidal categories and showed that if the monoidal category is a unique factorization category, then the plus construction yields a Feynman category. In this paper, we will focus on different methods for constructing UFCs and demonstrate how the plus construction reproduces and clarifies many existing constructions through explicit computations.