Jonathan wrote:

> These are the two instances I lean on more.

Right, me too usually. But when I discuss "resource theories", I start wanting "greater than" to mean something like "having more resources", or more money. So, I started out by flip-flopping between conventions when discussing Chapter 2, but I am now trying to consistently use a convention where \\(x \le y\\) means "you can get \\(x\\) from \\(y\\)". I think we're doomed to think about opposite categories (or at least "opposite posets") no matter what convention we choose, but I think beginners will find

$$ \textrm{ cake } \le \textrm{ cake } + \textrm{ ice cream } $$

less confusing than

$$ \textrm{ cake } + \textrm{ ice cream } \le \textrm{ cake }$$

Luckily, it's just a convention so it doesn't really matter.