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Monday, September 20, 2004

I'm pretty happy with Category theory right now. You ever get that nagging feeling that all these seemingly disparate concepts are related? Ever think there should be a more formal way of defining the free group on a set X (more formal than saying "it's the group on X without any other restrictions)? How about a way of rigorizing the notion of a "natural" map, ie. the naturalness of the double dual operator x^(f) = f(x) ? It's all in category theory! It's like I'm discovering all this previously mysterious machinery which underlies everything one does in math. Great stuff.
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