To remember the condition for lax vs. oplax monoid monotone functions, I'm testing out this mnemonic:

Lax - doing things separately is cheaper than doing them together
Oplax - doing things together is cheaper than doing them separately

Lax functions are like relaxed people (i.e. people with time during the week) who find it easier to clean 10 minutes every day instead of cleaning for 1 hour once a week.