on https://en.wikibooks.org/w/index.php?title=Haskell/Category_theory&stable=0#Hask.2C_the_Haskell_category the second exercise in the box (see illustration there) asks "(Harder.) If we add another morphism to the above example, it fails to be a category. Why? Hint: think about associativity of the composition operation." There are no answers-to-exercises. Can someone explain to me why adding another function with the same type causes the Haskell type system to no longer form the Hask category? (scratching head)
You're misreading the question. It's asking you to show that the category
induced by the <= relation fails associativity if you add an extra
morphism.
On Mar 29, 2014 1:19 AM, "John M. Dlugosz"
on https://en.wikibooks.org/w/index.php?title=Haskell/ Category_theory&stable=0#Hask.2C_the_Haskell_category
the second exercise in the box (see illustration there) asks "(Harder.) If we add another morphism to the above example, it fails to be a category. Why? Hint: think about associativity of the composition operation."
There are no answers-to-exercises. Can someone explain to me why adding another function with the same type causes the Haskell type system to no longer form the Hask category?
(scratching head)
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On Sat, Mar 29, 2014 at 12:18 PM, John M. Dlugosz
"(Harder.) If we add another morphism to the above example, it fails to be a category. Why? Hint: think about associativity of the composition operation."
One has to be careful with crowd-sourced wikipedia-like learning material. They aren't always helpful, although 80% of the time they are. In this case, the 2 exercises probably belong right after the section on "Category Laws" but _before_ "Hask, the Haskell category." That way, there's less confusion about what the exercises refer to and what they do NOT refer to. They certainly don't refer to Hask. That said, the exercises presume acquaintance with partial orders / posets so there's some web-trawling to be done if the requirement is unmet. And I'll also argue that the exercises aren't helpful. They may have their place in some musty math textbook. But for a general audience, it's like having some obscure concept (category) explained in terms of another obscure concept (partial order), with no-one getting any wiser. p.s. if you are still stuck email me off-list for the answer. -- Kim-Ee
participants (3)
-
Arjun Comar -
John M. Dlugosz -
Kim-Ee Yeoh