Q:

Galois connections between quasi orders?

A binary relation over a set $A$ is a quasi order if it is reflexive and transitive. It would be a partial order if it also were anti-symmetric.
I've always seen Galois connections be defined over partially ordered sets. I can immagine a similar concept defined over quasi ordered sets as well. 
Is the concept of Galois connection between quasi ordered sets meaningful/interesting? Has it been studied and if so where can I find some references?

A:

Galois Connections Presented Calculationally by C.J. Aarts gives a wonderfully accessibly introduction to the theory along with clear proofs and flurry of examples.
It can be found online at: http://www.cs.nott.ac.uk/~psarb2/MPC/galois.ps.gz
Roland Backhouse has a host of material on Galois Connections and is promoter of their use in computing science. See his site for many lovely articles: http://www.cs.nott.ac.uk/~psarb2/papers/papers.html

