[Haskell-cafe] adjunction of product and exponentiation
Jason Dusek
jason.dusek at gmail.com
Wed Aug 6 16:56:08 EDT 2008
The problem as stated is to find the unit for the adjunction:
((- x A), (-)^A x A)
The latter functor takes an arrow f to (f . -) x id_A and does
the obvious thing for objects. The co-unit diagram is given
as:
B^A x A ---- eval_AB ----> B
^ ^
| |
| |
curry(g) x id_A g : C x A -> B
| |
| |
| |
C x A --------------------+
This diagram is somewhat puzzling, because it seems the second
functor has turned into (-)^A ! Continuing in with that, we
get a unit diagram like this:
C ---- magic ----> (C x A)^A
| |
| |
| |
curry(g) (g . -)
| |
| |
| v
+------------------> B^A
So what is the magic? It is an arrow that takes a C to an
arrow that takes an A and makes the product C x A. I want to
write curry(C x A) but that is ridiculous looking. What's the
right notation for this thing?
--
_jsn
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