21/06/2006, 11:00 — 12:00 — Room P3.10, Mathematics Building Isar Stubbe, Centro de Matemática da Universidade de Coimbra
-orders and -modules
It is well known that the internal sup-lattices in the topos of sheaves on a locale are precisely the modules on that locale. I shall show a generalization of this result to the case of ordered sheaves on a quantaloid. A quantaloid is the "many-object version" of a quantale (which is more-or-less a "non-commutative locale"), and a module on a quantaloid is the obvious generalization of the common notion of module on a quantale. On the other hand, an ordered sheaf on a quantaloid should be thought of as an ordered set in a universe governed by a logic whose truth values are the arrows of the quantaloid. This subject thus has strong links with non-commutative topology, (linear or rather "dynamic") logic, order theory, and (enriched) category theory. I shall try my best to avoid technicalities and concentrate rather on getting across the main ideas.
