hi, the reference for the discussed fact is @article{FoxT:cartesian, author = {Thomas Fox}, title = {{Coalgebras and cartesian categories}}, journal = {Communications in Algebra}, volume = {4}, year = {1976}, pages = {665--667}, issue = {7}, doi = {10.1080/00927877608822127}, } sorry about lagging behind. it is interesting how forgetting leads to new discoveries :) -- dusko On Mar 12, 2013, at 11:09 PM, Chris Heunen wrote:
Dear Claudio,
One place with a spelled out proof that you could refer to is Theorem 2.1 of http://dx.doi.org/10.1016/j.entcs.2008.10.012: Let (C,+,0) be a symmetric monoidal category. Then (+,0) provides finite coproducts if and only if the forgetful functor cMon(C)->C is an isomorphism of categories.
At that point I, like you, couldn't find any references, but I'm sure it is a well-known piece of folklore, and would be interested if you can trace its earliest appearance in the literature.
Best wishes, Chris
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