[Haskell-cafe] A quick question about distribution of finite maps.

宮里洸司 viercc at gmail.com
Sat Jan 9 16:42:09 UTC 2021

Hi Ignat, would you slow down a bit and tell us the idea behind your

You seem to expect Map forms a Cartesian closed category, and
want to know if the specific property of CCC holds ("functors of shape (a ⇸ -)
are distributive".)

Could you explain that expectation step-by-step? For the first step, let us know
the category made from Maps more clearly. I mean, (1) what are the objects
of that category? (2) what are the morphisms? (3) how the identity morphisms
and the composition of morphisms are defined?

The next step would be the "Cartesian" part. This category should have
direct product of any finite number of objects. What exactly are these,
and how do you define the projection morphisms (equivalents of `fst` and
`snd` in your category) and the product of morphisms (equivalent of `&&&`.)

It's too rushed to think about CCC until these aren't clear.

/* Koji Miyazato <viercc at gmail.com> */

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