[Haskell-cafe] adjoint of coproduct & diagonal

Jason Dusek jason.dusek at gmail.com
Sun Aug 3 17:37:50 EDT 2008

Derek Elkins <derek.a.elkins at gmail.com> wrote:
> Jason Dusek wrote:
>> What about the part that reads:
>>     The unique arrow f making this diagram commute is then
>>     correspondingly denoted f1 ∐ f2 or f1 ⊕ f2 or f1 + f2 or
>>     [f1, f2]
>>   This would seem to say that [f,g] and f+g are the same thing
>>   -- but if I've understood Derek Elkins' remarks, the latter is
>>   the functorial action on arrows while the former is just the
>>   mediating arrow.
> In my experience the functorial action of a functor on arrows almost
> always has the same symbol as the action on objects.  Furthermore, I
> don't think I've ever seen an example where the symbol used for the
> action on objects was used for something other than the action on
> arrows.  I do think I have seen examples when a different symbol was
> used.  If A+B is used then f+g should be the action on arrows.
> Admittedly wikipedia does violate this. Perhaps it's using conventions
> from some branch that I'm not familiar with. Maybe it is just silly.

  Indeed. Using f1 ∐ f2 or f1 + f2 for the mediating arrow is
  confusing, to say the least.


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