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Stop pretending studying arrow theory improves your apping

Name: Anonymous 2015-03-11 7:12

Given two functors S,T:C→B, a natural transformation τ:S→T is a function which assigns to each object c of C an arrow τc=τc:Sc→TC of B in such a way that every arrow f:c→c' in C yields a diagram
ᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠτc
c ᅠᅠ Sc---→Tc
|ᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠᅠᅠᅠᅠ|
|fᅠᅠᅠᅠᅠSf↓ᅠᅠᅠᅠᅠ↓Tf
↓ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠτc'ᅠᅠ|
c', ᅠᅠᅠ Sc'--→Tc'


which is commutative. When this holds, we also say that τc=τc:Sc→Tc is natural in c. If we think of the functor S as giving a picture in B of (all the objects and arrows of) C, then a natural transformation τ is the set of arrows mapping (or, translating) the picture S to the picture T, with all squares (and parallelograms!) like that above commutative:
ᅠaᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠSa----------→Ta
ᅠ|ᅠ╲fᅠᅠᅠᅠᅠᅠᅠ ᅠ|ᅠ╲Sfᅠᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠ╲Tf
ᅠ|ᅠᅠᅠ↘ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ↘ᅠᅠᅠτbᅠᅠᅠ|ᅠᅠᅠ↘
ᅠ|ᅠᅠᅠᅠᅠbᅠᅠᅠᅠ ᅠ|ᅠᅠᅠᅠSb----------→Tb
ᅠ|ᅠᅠᅠ╱ᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ╱ᅠᅠᅠᅠᅠᅠᅠᅠᅠ|ᅠᅠᅠ╱
↓ᅠ↙ᅠᅠᅠᅠᅠᅠ ᅠ↓↙Sgᅠᅠᅠᅠᅠᅠᅠᅠ↓ᅠ↙Tg
ᅠcᅠᅠᅠᅠᅠᅠᅠᅠᅠᅠSc----------→Tc

Name: Anonymous 2015-03-11 22:41

>>15
There is a lot wrong with haskell as a community and the language is being destroyed but the new crowd. Their watered down version of category theory is also quite sad.

monads are important in programming but I'm always surprised how bad haskell programmers are with them and transformers. It's pretty distressing.

I was just checking earlier if there was a nice persistent data structure on hackage and the first one I looked at uses unsafePerformIO.

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