Oh, if products and coproducts coincide, then
you can define addition of morphisms nicely. Cool.
Y'know, if someone studies a foreign language
intensely, especially to the point of
fluency, it (I would think) ought come as
no surprise that they start involuntarily
thinking -in- that language even when unnecessary
for communication, thinking in terms of idioms
and semantic niches not present in their native
language, etc. And yet I -am- surprised (and
even kind of embarrassed or annoyed, though
I'm not sure I need to be) each time I think of
some everyday concept in terms of some technical
CS, mathematical, philosophical, or just
generally geekish construct, even though I
spend the majority of my waking hours 'speaking'
these languages in one form or another.