\begin{definition}[Definition:Category of Open Sets/Definition 1]
Let $T = \struct {S, \tau}$ be a topological space.
The '''category of open sets''' of $T$, denoted $\map {\mathbf {Ouv} } T$, is the small category with:
{{DefineCategory
| ob = open sets of $T$
| mor = inclusion mappings between subsets, none otherwise
| comp = composition of mappings
| id = identity mappings
}}
\end{definition}