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.

Reference

Wikipedia: Sheaf

Parents

Element of

Cat, Thin category