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The article argues against overly formal approaches, but I actually think it errs too much in that direction. When I'm studying a math thing, at some point I ne
by daffodil2 12y ago
The article argues against overly formal approaches, but I actually think it errs too much in that direction. When I'm studying a math thing, at some point I need you to shut up with the English words and simply describe the object in terms of sets, functions, relations and properties. Categories stopped being mysterious for me once I realized they were just multigraphs with a certain algebraic operation defined on edges (composition) such that edges with certain properties (identities) were stipulated to exist.
- kybernetikos 12y agoI suspect that that explanation only works on people with a fairly specific background. I think the hope of the article is to target a wider range of people who could benefit from understanding the formalism.
- nilkn 12y agoI feel that you have to be careful with that definition insofar as the objects in a category may not form a set at all but a proper class.
- rfrey 12y ago"Categories are just multigraphs with composition and stipulated identities on edges, what's the problem?" Just kidding, I appreciate the trailhead. :)
- sanderjd 12y agoHa, I actually read his last sentence as sarcasm initially and thought "haven't I heard this joke..." only to find that you had already referenced the one I was thinking of: "A monad is just a monoid in the category of endofunctors, what's the problem?"
- daffodil2 12y agoI didn't mean to imply it was trivial to understand, but it's no more difficult than the formal definition of, say, a derivative (which involves a limit, and hence an epsilon-delta construction, which in my experience are not so easy to fit in your head at first). Understanding what a multigraph is should be doable.
- sanderjd 12y agoI totally agree with you, but jargon of all kinds just sounds funny to people unaccustomed to it, regardless of its difficulty to understand!