\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)

Maximal and minimal elements, definition

Let \( X \) be a partially ordered set, and let \( Y \) be a subset of \( X \).

Minimal element

We say that \( y \) is a minimal element of \( Y \) if [...].

Maximal element

We say that \( y \) is a maximal element of \( Y \) if [...].