locales

Noun

locale (plural locales)

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. 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. 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 #92;mbox#123;Sub#125;#95;#92;mathcal#123;E#125;(1) [subobjects of the terminal object in #92;mathcal#123;E#125;] for some topos #92;mathcal#123;E#125;, locale theory can be regarded as the fragment of topos theory concerning subobjects of 1. A subobject of 1 is a...2011 June 27, Tom Leinster, “An informal introduction to topos theory”, in arXiv.org, Cornell University Library, retrieved 21 Mar 2018