If C is an ordered symmetric monoidal closed category (i.e. has a tensor such that X \tensor (_) has a right adjoint) then the category ICMon(C) of idempotent commutative monoids over C (such that the monoidal operation preserves the order in a sensible way) forms a category that can behave like the category of frames. Take for example C= Sup lattices, or C = Preframes and ICMon(C) is, in both cases, equivalent to the category of frames. I was therefore trying to look at ICMon(C)^op for any symmetric monoidal C, and see how well Locale theory can be done in this category. Does anyone have any suggestions about how a flat sublocale may be axiomatised in this setting? Thanks Christopher [i: X_0 >-> X (a regular monic in the category of locales, i.e. a sublocale) is flat iff the corresponding nucleus preserves finite joins] _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp 26-Jul-2001 17:56:25 -0300,4460;000000000000-0000001f