Well-supported object
= Well-supported object
An object of a <regular category> is well-supported when its <support of an object in a regular category> is the <terminal object>, equivalently when $A\to1$ is a <regular epimorphism>. Finite products of well-supported objects are well-supported, by pullback and composition stability of regular epimorphisms. A regular epimorphism has the same support as its codomain, and an object with a point $1\to A$ is well-supported.