Centrality and the commutativity of finite products with coequalisers

TL;DR

This paper investigates the properties of central morphisms in categories where binary products commute with coequalisers, extending known results from unital categories to broader contexts.

Contribution

It generalizes the behavior of central morphisms from unital categories to categories where binary products commute with coequalisers, including weakly unital and non-unital categories.

Findings

Central morphisms behave similarly in broader categories as in unital categories.

Much of the known behavior of central morphisms is retained outside unital settings.

The study extends the understanding of categorical structures where products and coequalisers interact.

Abstract

We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that much of the behaviour of central morphisms for unital categories is retained in our setting, including categories which are (weakly) unital, but also categories outside of the unital setting.