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Getting Started with Category Theory
s a fascinating and unreasonably powerful tool for thinking about computation, transformation, and relationships between things in the world. That makes it useful for mathematicians, computer scientists, and philosophers alike.
For example, imagine the collection of all possible states our world could be in (Einstein being the American president, dogs not existing, and any other wacky thing you can come up with). I won't properly define exponential objects until later on when I discuss products and universal constructions, but just knowing about them informally helps one realize the depth with which one can think about arrows in a category. Composition in these categories are addition and multiplication respectively, and the functor is raising 2 to a power, so the functors-preserve-composition equation \(F(g\circ f)=Fg\circ Ff\) becomes \(2^{n+m}=2^ncdot 2^m\), a rule for exponentials we learn in high school!
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