30 Oct
1998
30 Oct
'98
9:26 a.m.
Can someone give me a reference for the fact that if the hom functor on a category factors through commutative monoids then finite products are sums and vice versa. Also conversely.
Michael
Mac Lane (Categories for the Working Mathematician) does one direction in Theorem 2 on page 190. (He assumes enrichment over abelian groups rather than commutative monoids, but a glance at the proof shows that the additive inverses are not used.) The converse is stated as Exercise 4 on page 194. Peter Johnstone