Sunday, September 26, 2010

Pullbacks

The videos posted by Catsters on youtube are really a great resource in learning Category Theory. The instructors have a sense of humor, and seem to be enjoying themselves. Unfortunately, I often am unable to understand the concepts given the formal nature of their discussions. The way I've been proceeding is to determine and then learn the specific concept that each idea in category theory generalizes. In one video the instructor suggests that you can either prove a claim they are talking about, or meditate about it in a categorical trance until you feel like you understand it. I've read of people having said that they do this very often (go into categorical trances), but I've never understood enough about the ideas to do so. Until now! I was able to understand a (admittedly trivial) concept in category theory (pullbacks) in at least some basic sense simply by thinking about the meaning of the associated commutative diagram.

A small victory, but a victory none the less.

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