What is an ideal a zero-class of?
N. Martins-Ferreira, A. Montoli, A. Ursini, and T. Van der Linden
TL;DR
This paper characterizes ideals as zero-classes of surjective relations within pointed regular categories and explores a variation of the 'Smith is Huq' condition related to commuting zero-classes.
Contribution
It provides a categorical characterization of ideals and investigates a new condition linking the commutativity of surjective relations and their zero-classes.
Findings
Ideals are characterized as zero-classes of surjective relations.
A variation of the 'Smith is Huq' condition is studied.
The relation between commuting surjective relations and their zero-classes is established.
Abstract
We characterise, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the "Smith is Huq" condition: two surjective left split relations commute as soon as their zero-classes commute.
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