> I don't always know the name of some mathematical object. I like making definitions and reasoning about them. Should I use a convention like this?
My issue was with you giving an established name -- unital quantale -- to something. It wasn't clear to me that your definition of unital quantale was one you'd just come up with or a definition from the literature. If you want to define something then give it a distinctive name! [A "unitalicious quantale" might work here amongst friends, but you might prefer something more circumspect if you were putting in a paper. :-) ]