\begin{definition}[Definition:Category of Pointed Sets]
The '''category of pointed sets''', denoted $\mathbf {Set}_*$, is defined as follows:
{{DefineCategory
| ob = pointed sets $\struct {A, a}$
| mor = pointed mappings
| comp = Standard composition of mappings
| id = $\mathrm {id}_{\struct {A, a} } := \mathrm {id}_A$, the identity mapping on $A$
}}
\end{definition}