Stop pretending studying arrow theory improves your apping

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 τ_c=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 τ_c=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

>>39

There's an implicit type mismatch

There is no type mismatch. Addition works only on operands of the same type. It is impossible to add an int to a double using the regular (+) method - you would have to make explicit casts. And yet this works:

Prelude> let x = 1.6
Prelude> let y = 2
Prelude> x + y
3.6