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May 24, 2015 at 5:57 vote accept Jens Reinhold
May 22, 2015 at 14:58 comment added Tyler Lawson I believe that the (generalized) Barratt-Priddy-Quillen would allow you to get an example with finitely generated set of components with the free symmetric monoidal category on an appropriate category (e.g. the coequalizer diagram $\bullet \rightrightarrows\bullet$)
May 22, 2015 at 8:57 history answered Neil Strickland CC BY-SA 3.0