Tobias wrote:

> The neat thing is that you can write every monoidal monotone as a combination of one of these: first, add capabilities; then, change the underlying set; then, discover new resources!

This sounds a lot like how every functor can be factored as one that only fails to be essentially surjective (but is full and faithful), one that only fails to be full (but is essentially surjective and faithful) and one that only fails to be faithful (but is essentially surjective and full). (Please don't ask me to remember in which order these 3 factors should arranged, I can do it but it's tiring.)