[Haskell-cafe] Intergalactic Telefunctors

[Tillmann Rendel]

Gregg Reynolds wrote:
> BTW, I'm not talking about Haskell's Functor class, I guess I should
> have made that clear.  I'm talking about category theory, as the
> semantic framework for thinking about Haskell.

In that case, I even less see why you are not introducing category 
theory proper. Certainly, if one wants to use a semantic framework for 
thinking about something, one should use the real thing, not some 
metaphors.

> The idea is that each type (category) is a distinct universe.  The essential
> point about functors cross boundaries from one category to another.

What are the categories you are talking about here?

>> Moreover, you are mixing in the subject of algebraic data types (all we
>> know about (a, b) is that (,), fst and snd exist).
>>
> 
> It's straight out of category theory.  See Pierce
> http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7986

Which part specifically?

>> Personally, I do not see why one should explain something easy like
>> functors in terms of something complicated like quantum entanglement.
> 
> The metaphor is action-at-a-distance.  Quantum entanglement is a vivid way
> of conveying it since it is so strange, but true.  Obviously one is not
> expected to understand quantum entanglement, only the idea of two things
> linked "invisibly" across a boundary.

How does the fact that a morphism exists between two objects in some 
category link these objects together? It doesn't change the objects at 
all. In your own words: How can action (at-a-distance) be about 
mathematical values?

   Tillmann