[Haskell-cafe] adjoint of coproduct & diagonal

Derek Elkins derek.a.elkins at gmail.com
Sun Aug 3 16:22:25 EDT 2008

On Sun, 2008-08-03 at 11:03 -0700, 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.
"Categories for the Working Mathematician" uses the convention I
describe here.  Although it doesn't seem to have a notation for the
mediating arrow (what I usually write as [f,g]).

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