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" 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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