Q-orders with no unit on Q
Chang-Jie Zhou, Wei Yao · Journal of Intelligent & Fuzzy Systems · 2021
For a usual commutative quantale Q (does not necessarily have a unit), we propose a definition of Q-ordered sets by introducing a kind of self-adaptive self-reflexivity. We study their completeness and the related Q-modules of complete lattices. The main result is that, the complete Q-ordered sets and the Q-modules of complete lattices are categorical isomorphic.