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Most of the article is about semi-lattices and posets which are often most usefully described in a categorical framework. Fibonacci sequence is just a toy examp
by ABeeSea 5y ago
Most of the article is about semi-lattices and posets which are often most usefully described in a categorical framework. Fibonacci sequence is just a toy example to demonstrate the general concept. I have a ton of graduate level math books that torture a toy example to death because they’re concrete.
- agumonkey 5y agoDo you know good articles about semi-lattices ?
- dbfkfndkjd 5y agoI'm pretty sure that what actually happened here is is that some category theory enthusiasts noticed a slightly surprising (and elementary) example of a commutative square in number theory. CT doesn't deal with number theory all that much. I came across this "commutative square" involving GCD and fib myself a couple of years ago. I came at it from noticing that there was a similar structure in iterative fib to the recursive Euclidean algorithm. Note the "a, b = b, a + b" def f(n): a, b = 0, 1 for i in range(0, n): a, b = b, a + b return a and then "a=b, b=a%b" here def gcd(a,b): if(b==0): return a else: return gcd(b,a%b) I googled "gcd fibonacci" and landed here: https://math.hmc.edu/funfacts/fibonacci-gcds-please/ https://math.hmc.edu/funfacts/fibonacci-gcds-please/
- ABeeSea 5y agoShe has a PhD in category theory. >Category Theory doesn’t deal with number theory all that much. Not sure where you are drawing the line here since algebraic geometry (aka modern number theory) makes extensive and extremely deep use of category theory. Ravi Vakil’s Rising Sea being the best intro to this point of view. This example is just a fun way to talk about posets.