4 ms·
Thank you for clarifying. I was familiar with the notation A^B for the set of all f: A -> B, but this seemed like something more (and it does appear to be). Pu
by epsilonclose 6y ago
Thank you for clarifying. I was familiar with the notation A^B for the set of all f: A -> B, but this seemed like something more (and it does appear to be).
Putting some links I looked at here to save someone a few seconds of Googling:
https://en.wikipedia.org/wiki/Exponential_object https://en.wikipedia.org/wiki/Exponential_object
https://ncatlab.org/nlab/show/exponential+object https://ncatlab.org/nlab/show/exponential+object
- dllthomas 6y agoI'm not sure if the notation you'd encountered differed, but in this case the equivalence is between A^B and B -> A (note the order). Interestingly, every identity you learned in grade school algebra which involved only addition, multiplication, and exponentiation holds here as an isomorphism. It can be a fun exercise to write the functions that take you back and forth. For instance: A^(B+C) = A^B * A^C to: (Either b c -> a) -> (b -> a, c -> a) to f = (f . Left, f . Right) fro: (b -> a, c -> a) -> (Either b c -> a) fro (f, g) = \case Left b -> f b Right c -> g c