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
