> My criticism, I think, is still valid. Just because you've renamed things in a bunch of fields with a consistently obtuse verbiage doesn't mean you've underst

> My criticism, I think, is still valid. Just because you've renamed things in a bunch of fields with a consistently obtuse verbiage doesn't mean you've understood anything It's unification, not renaming. As a somewhat tortured analogy, consider two concepts: "games", and "mass". Particular concrete games are prior to "games" in general: we learn nothing about chess or basketball by noting that we happen to have a label broad enough to include both, and the worldview of an alien visitor accustomed to thinking only in terms of board-games or ball-games but never simply games is simply different, not incomplete. But if someone has concepts for mass-of-people and mass-of-planets but doesn't realize that they're all instances of a more general notion of mass-of-things, the situation is different. People-mass and planet-mass are both "mass" not only by convention, as with games, or by brute coincidence, but by physical law. And someone who doesn't know that has a hole in their understanding of physics. Category-theoretic concepts should be understood in the latter sense. Expecting knowing what a monoid is to deepen your understanding of string concatenation, for instance, is getting things backwards. (This is really an example from abstract algebra, not category theory proper, but the same principle applies). The point is to use your knowledge of string concatenation to get knowledge about {string concatenation | linked lists | regular expressions | MapReduce | max/min | addition | multiplication | convex hulls | ... }, all at once and (once you've paid the upfront cost) all for free.