[Haskell-cafe] The meaning of categories constructed from HASK
David Feuer
david.feuer at gmail.com
Fri Sep 23 05:50:51 UTC 2016
It's generally quite hard or impossible to express commutative diagrams as
Haskell types since it's (currently) impossible to talk about term equality
at the type level. I imagine someone who actually knows category theory can
describe some ways they use such concepts to design or analyse Haskell
code, though.
On Sep 22, 2016 7:26 PM, "Dimitri DeFigueiredo" <defigueiredo at ucdavis.edu>
wrote:
> In category theory, there are many ways one can make new categories out
> of an old one.
>
> In particular, given a category C one can construct:
>
> 1. The arrows category of C:
> arrows in C become objects and
> commutative squares in C become arrows
> 2. The slice category of C given an object A:
> arrows into a distinguished object A become objects in the slice
> commutative triangles become arrows
>
> There are also functors going from C to these new categories (and back).
>
> Are these constructed categories useful when C = `Hask` (the category of
> haskell types and functions)?
> What do they represent in programming terms?
>
> In other words, is there intuition for what the arrows category of Hask is?
> What about the slice category of Hask over a specific type?
> Do the functors between these match some programming abstractions?
>
> Any pointers are much appreciated.
>
> Thanks,
>
> Dimitri
>
>
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