CAUTION: The Sender of this email is not from within Dalhousie. I do not have a reference, but I think these are precisely the complete boolean algebras. Glue two copies of the locale X along an open subset U, and call the result Y. Then Y can be seen as an object of Sh(X). The intersection of the two copies of X inside Y is equal to U (from one of Giraud's axioms). On the other hand, we can write Y as a sum of open subsets of X (the "terms" of Y). And we can similarly write X as a sum of open subsets ("terms") such that each term of X gets mapped into a term of Y. Now we can compute U as the sum of those terms of X that are mapped to the same term of Y along the two inclusions in Y. The disjoint union of the other terms of X then form the complement of U. Best regards, Jens ---------- Forwarded message --------- From: <streicher@mathematik.tu-darmstadt.de<mailto:streicher@mathematik.tu-darmstadt.de>> Date: Tue, 9 Jun 2020 at 00:21 Subject: categories: locales such that the associated topos is subdiscrete? To: <categories@mta.ca<mailto:categories@mta.ca>> Toposes Sh(B) of sheaves over a cBa B have the property that every object appears as sum of subterminals. Does any one know a more elementary characterization of those cHa's A such that every object of Sh(A) appears as sum of subterminals? Maybe it is precisely the cBa's but I do not see how to prove it... Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]