The Category of Finite Incidence Posets

Abstract

In the dissertation \textit{A Study on the Category of Graphs}, Buvaneswari constructs the category of finite, simple graphs and determines the existence of particular, categorical objects within the same. We use Buvaneswari's dissertation as the basis for an investigation into the category of finite incidence posets, which we construct herein. We prove that the category of finite, simple graphs is equivalent to the category of finite incidence posets, and we prove the existence of equalizers, products, and coproducts in the category of finite incidence posets.