Lagois Connections - a Counterpart to Galois Connections

In this paper we deene a Lagois connection, which is a generalization of a special type of Galois connection. We begin by introducing two examples of Lagois connections. We then recall the deenition of Galois connection and some of its properties; next we deene Lagois connection, establish some of its properties, and compare these with properties of Galois connections; and then we (further) develop examples of Lagois connections. Via these examples it is shown that, as is the case of Galois connections, there is a plethora of Lagois connections. Also it is shown that several fundamental situations in computer science and mathematics that cannot be interpreted in terms of Galois connections naturally t into the theory of Lagois connections.