locale

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.
   • Small houses have sprung up as rapidly as the summer grasses used to spring in the Five Fields, so notorious for robbery and murder, that even Madame de Genlis, not usually very accurate in her English locale, is perfectly right in making them the scene of a robber's attack.1837, L[etitia] E[lizabeth] L[andon], “Changes in London”, in Ethel Churchill: Or, The Two Brides. […], volume II, London: Henry Colburn, […], →OCLC, page 231
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