A Small Observation on Co-categories

TL;DR

This paper investigates the nature of co-categories within coherent categories, revealing that all co-categories in such contexts are necessarily co-equivalence relations, highlighting a specific structural property.

Contribution

It establishes that in coherent categories, co-categories are always co-equivalence relations, providing a precise characterization of their structure.

Findings

All co-categories in coherent categories are co-equivalence relations.

The result clarifies the internal structure of co-categories in categories with strong logical properties.

The paper offers a concise insight into the nature of co-categories in a specific categorical setting.

Abstract

Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.