Lattices in Dedekind Categories
Yasuo Kawahara · Studies in fuzziness and soft computing · 2001
Lattice structures are fundamental and useful in mathematics and theoretical computer science. It is well-known that lattice structures with meet and join operations satisfying associative, commutative and absorption laws are equivalent to lattice structures defined by ordering relations having joins and meets. This paper defines a notion of lattices in Dedekind categories and studies some basic properties of lattice structures. Following relational calculus, an element-free representation of these properties is discussed.