I'm working on Exercise 8.16 from http://web.mit.edu/18.705/www/syl11f.html. In particular:
Let F : ((R-mod)) → ((R-mod)) be a linear functor. Show that F always preserves finite direct sums. ...
The solution provided says:
The first assertion follows immediately from the characterization of finite direct sum in terms of maps (4.15), since F preserves the stated relations. ...
Unfortunately I can't discern anything from (4.15) [which I think is an incorrect link] or anything from its surroundings. I feel like I'm missing something simple. I don't see any way to relate F(direct sum) to direct-sum(F).