No, not really, it isn't

...someone in TQFTs class today thought analogy/joke about a category being a monoid with many objects was literally true, and was asking to try to understand just what sort of monoid a category was, before Peter May finally realized the guy thought a category was actually a monoid [I should note here, I didn't realize that was what was going on] and told him it wasn't actually a monoid at all. Kind of bizarre.