[Haskell-cafe] adjoint of coproduct & diagonal
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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