 Subterminal object

An object $S$ is subterminal when its unique morphism $S\to 1$ to the terminal object is a monomorphism. Equivalently, every object has at most one morphism to $S$. Subterminal objects form the preorder $\mathrm{Sub}(1)$.

In category theory, a **subterminal object** is a specific type of object that generalizes the notion of a "singleton" in a categorical context. To understand it, let's first define a few key concepts: 1. **Category**: A category consists of objects and morphisms (arrows between objects) that satisfy certain properties (closure under composition, associativity, and identity).