Weights for Monoids and Actions of Monoids

TL;DR

This paper introduces a categorical framework for monoids and their actions by defining their categories as weighted limits, providing a new perspective on their structural properties.

Contribution

It formalizes the categories of monoids and monoid actions as weighted limits, offering a novel categorical approach to these algebraic structures.

Findings

Categories of monoids are characterized as weighted limits.

Actions of monoids along monoidal categories are also described as weighted limits.

Provides a new categorical perspective on monoid structures and their actions.

Abstract

The main objective of the paper is to define the category of monoids as a weighted limit. We also define the category of actions of monoids along the action of a monoidal category as a weighted limit.