> You guys are no fun. lol

_Au contraire_, you're simply late to the party. ;D

Ok, let's try something else.

**Puzzle JMC8** (unsolved): What do we get if we enrich over the lattice given by \$$\\{\bot \le \mathrm{false} \le \top, \bot \le \mathrm{true} \le \top\\}\$$, with identity \$$\mathrm{\bot}\$$ and monoidal operator given by join (\$$\vee\$$)? Some questions I've been looking at myself work over similar structures, so it might be fun to see if we get anything interesting when we enrich by them.

(In particular, the preorder here is an [elementary domain](https://en.wikipedia.org/wiki/Domain_theory#Special_types_of_domains) (plus a top element); there are many other domains, and we generally like to look at [directed-complete partial orders](https://en.wikipedia.org/wiki/Complete_partial_order).)