Hi - Paul Blain Levy writes: It seems to be folklore that
(1) symm(C) is the free symmetric monoidal category on C
(2) coaff(C) is the free coaffine category (symmetric monoidal category
with initial unit) on C.
[....]
But for general C, where are these statements proved? I'll admit to having used the first statement without proof on page 14 here: http://arxiv.org/abs/q-alg/9702014 As I get older I feel worse about doing such things. Perhaps an efficient proof of both statements could be developed from here: Symmetric monoidal sketches Martin Hyland and John Power https://www.dpmms.cam.ac.uk/~martin/Research/Oldpapers/hp00.pdf Theorem 2.5 gives the free symmetric monoidal category on a "symmetric monoidal sketch". Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]