A lattice is a latch. A latice theory is the theory that if you lock it, they will come.

There was a fable about a country on the edge of starvation. The nobles hoarded goods and the peasantry was growing resentful. To save their country from falling apart, officials imported foreign foods/seeds and distributed them freely among the masses. Unfortunately, the peasantry was already very suspicious and thought the aristocracy was trying to poison them so they wouldn’t share any of the real food and rejected the gesture. Instead they began robbing and looting.

With little time to waste, one official came up with an idea. The peasantry didn’t trust wealth given freely, so why not treat the imported stuff as valuables and have the peasants rob that instead? So they made fake convoys filled with the stuff and let the masses rob as much as they wanted. In the end, the peasantry took to the foreign foods/seeds like ducks to water, the country was saved and the aristocunts immediately began to exploit the new products, which caused a revolution and the end of the monarchy. The end.

As you can probably tell by now, none of it is true, but I felt like writing it, so you’re welcome.

It’s just a set where you can define “join” and “meet” operations that follow the lattice laws.