## Category of open sets

### Set

 context $\langle X,\mathcal T\rangle$ … topological space inclusion $\mathrm{Op}(X)$ … category definition $\mathrm{Ob}_{\mathrm{Op}(X)}\equiv \mathcal T$ for all $V,U\in\mathrm{Ob}_{\mathrm{Op}(X)}$ definition $\mathrm{Op}(X)[V,U]\equiv\{i:V\to U\ |\ i(x)=x\}$

### Discussion

In the category of open sets, the arrows are the inclusion functions. In the case $V\subseteq U$, the hom-set $\mathrm{Op}(X)[U,V]$ is the singleton $\{i\}$ and otherwise it's empty.

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