Communications of the
Korean Mathematical Society CKMS

Using idempotents in quasi-lattices, we show that the category {\bf Latt} of lattices is both reflective and coreflective in the category {\bf qLatt} of quasi-lattices and homomorphisms. It is also shown that a quasi-ordered set is a quasi-lattice iff its partially ordered reflection is a lattice.

Keywords: quasi-lattices, idempotents, reflection, coreflection

MSC numbers: 06A06, 06B99, 18A40, 18C05