Object - Imported Knowlpedia Content

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

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