[Haskell-cafe] Intergalactic Telefunctors
Tillmann Rendel
rendel at cs.au.dk
Sun Feb 15 12:53:36 EST 2009
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
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