On Morita Equivalence of Partially Ordered Monoids

摘要

We show that there is one-to-one correspondence between certain algebraically and categorically defined subobjects, congruences and admissible preorders of S-posets. Using preservation properties of Pos-equivalence functors between Poscategories we deduce that if S and T areMorita equivalent partially orderedmonoids and F: PosS → PosT is a Pos-equivalence functor then an S-poset AS and the Tposet F(AS) have isomorphic lattices of (regular, downwards closed) subobjects, congruences and admissible preorders. We also prove that if AS has some flatness property then F(AS) has the same property.