Definition of "locale"

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, […], page 231

Since every locale is of the form Sub E ( 1 ) {\displaystyle {\mbox{Sub}}_{\mathcal {E}}(1)} [subobjects of the terminal object in E {\displaystyle {\mathcal {E}}} ] for some topos E {\displaystyle {\mathcal {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 {\displaystyle 1\rightarrow \Omega } , which can reasonably called a truth value. In that sense, locale theory is the study of truth values.

2011 June 27, Tom Leinster, “An informal introduction to topos theory”, in arXiv.org‎, Cornell University Library, retrieved 2018-3-21