/sci/ - Science & Math

Hey, I need some help with a seemingly-simple problem in category theory that I can't resolve.

I am trying to find a general way of representing the colimit (resp. limit) of a diagram in a category with an isomorphic object that is the limit (resp. colimit) of a separate diagram. An exercise I am trying to work on this generalization is simple to explain:

Let A, B be objects in Set. Let AUB be their coproduct. Now, we can represent AUB also as the set of tuples (x,Y) in (AUB)x{A,B} such that x is in the image of the injection of Y into AUB. This is obvious, but it signaled to me that we are looking at a specific kind of limit, because pullbacks in Set look like subsets of various S where various maps with codomain S agree.

My question is: what diagram is this the pullback (or some similar breed of limit) of? I feel like the subobject classifier, call it {0,1}, is going to be somewhere in the diagram because it helps us classifies when certain qualities hold (the element inclusion either holds or doesn't). Maybe somebody could offer some insight.

I feel like this should just be obvious to me, but I can't get my brain to spit out an answer this time.

Thanks for the time, guys!

/sci/, I need your help.

There's this girl, and I've come to care for her quite a bit.
She hasn't been fortunate enough to have a positive upbringing though. And what I mean is, her parents were hardcore christians that sent her to bible camp, rather than space camp. And she managed to break free of those silly religious tethers, but fell into the hole of things such as astrology, spirit science, homeopathy, and countless other new age trendy culty bullshit. Admittedly, I used to believe in spirit science, but once I pulled my head out of my ass and played devil's advocate for a little bit, it became clear rapidly how stupid all of it was.

Now, she may be caught up in all this bullshit, but she's honestly a very smart girl. You know how you can recognize intelligence in people through humor, or art, or even just regular socializing? She's been over many nights, and I'll be showing her things on the computer, like how to torrent files, troubleshoot faulty mp3 players, change the oil in her car, etc etc, and she tackles it with exuberance and confidence.
And I feel like that energy and intelligence could be put to much better use than this new age shit.

She's going to school in western canada this fall to do some phytotherapy/holistic nutrition dual 'degree' bullshit. Here's the link:
http://www.pacificrimcollege.com/faculties-programs/program/dual-diplomas-of-phytotherapy-and-holistic-nutrition/

I've already opened her eyes to the scam of a company she's currently working for, and now that she realizes it, she's planning on jumping ship from them. But she's jumping to another burning one.

So I ask you guys, can you help me make a brief, diplomatic, concise article that outlines the who, what, when, where, why, and how of how all this shit is bullshit?