Hi Owen,

It's amazing that you came up with your insights in [#1](https://forum.azimuthproject.org/discussion/comment/17342/#Comment_17342) by yourself. That's definitely Formal Concept Analysis at work.

Regarding the Galois connection in [#5](https://forum.azimuthproject.org/discussion/comment/17342/#Comment_17342) that John noted, an small but formal exposition with proof, example and diagrams can be found in Amanda Bower, [Category theory and Galois theory](http://math.ucr.edu/home/baez/qg-fall2015/amanda_bower_category_theory_and_galois_theory.pdf), [Rose-Hulman Undergraduate Mathematics Journal](https://www.rose-hulman.edu/mathjournal/v14n1.php) 14 (2013), 134–142.