[Haskell-cafe] What do you call Applicative Functor Morphism?

Ben midfield at gmail.com
Sat Nov 6 16:48:02 EDT 2010

category theory encompasses more than just algebra.  so there are homomorphisms, but also diffeomorphisms, symplectomorphisms, et cetera (in addition to things which don't have the -morphism suffix in normal usage, like continuous maps, natural transformations.....)


On Nov 6, 2010, at 7:19 AM, roconnor at theorem.ca wrote:

> On Sat, 6 Nov 2010, Sebastian Fischer wrote:
>> Hello,
>> I'm curious and go a bit off topic triggered by your statement:
>> On Nov 6, 2010, at 12:49 PM, roconnor at theorem.ca wrote:
>>> An applicative functor morphism is a polymorphic function,
>>> eta : forall a. A1 a -> A2 a between two applicative functors A1 and A2 that preserve pure and <*>
>> I recently wondered: why "morphism" and not "homomorphism"?
> Morphisms can be more general than homomorphisms.  But in this case I mean the morphisms which are homomorphisms.  I was too lazy to write out the whole word.
> -- 
> Russell O'Connor                                      <http://r6.ca/>
> ``All talk about `theft,''' the general counsel of the American Graphophone
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