locale

Etymology

From French local (adj), nominal use of the adjective.

noun

1. The place where something happens.
   Being near running water and good shade, the explorers decided it was a good locale for setting up camp.
2. (computing) The set of settings related to the language and region in which a computer program executes. Examples are language, currency and time formats, character encoding etc.
3. (mathematics) A partially ordered set with the following additional axiomatic properties: any finite subset of it has a meet, any arbitrary subset of it has a join, and distributivity, which states that a binary meet distributes with respect to an arbitrary join. (Note: locales are just like frames except that the category of locales is opposite to the category of frames.)
   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. 2011-6-27, Tom Leinster, “An informal introduction to topos theory”, in arXiv.org, Cornell University Library, retrieved 2018-03-21