locale

Being near running water and good shade, the explorers decided it was a good locale for setting up camp.

Since every locale is of the form mbox Sub_( mathcal )E(1) [subobjects of the terminal object in ℰ] for some topos ℰ, locale theory can be regarded as the fragment of topos theory concerning subobjects of 1. A subobject of 1 is a map 1→𝛺, which can reasonably called a truth value. In that sense, locale theory is the study of truth values.