Object

Definition

Let $\mathcal C$ be a category . An object of $\mathcal C$ is an element of the collection $\mathrm{Ob}(\mathcal C)$.

An object has no “internal data” in the definition beyond belonging to $\mathcal C$; its properties are typically expressed by the pattern of morphisms to and from it.

Examples

1. In $\mathbf{Set}$, an object is a set .
2. In $\mathbf{Grp}$, an object is a group.
3. In $\mathbf{Top}$, an object is a topological space.