Presenting Finite Posets

TL;DR

This paper introduces a monoidal category of finite partial orders with specific source and target elements, providing a presentation that relates to a variant of bialgebra, enriching the categorical understanding of posets.

Contribution

It constructs a presentation of a monoidal category of finite posets using generators and relations, linking it to a variant of bialgebra.

Findings

Defines a monoidal category of finite partial orders with designated minimal and maximal elements.

Provides a presentation of this category via generators and relations.

Connects the categorical structure to a variant of bialgebra.

Abstract

We introduce a monoidal category whose morphisms are finite partial orders, with chosen minimal and maximal elements as source and target respectively. After recalling the notion of presentation of a monoidal category by the means of generators and relations, we construct a presentation of our category, which corresponds to a variant of the notion of bialgebra.