Dear Andrej, Here are a few: 1. It's the symmetric monoidal category freely generated by a pointed object (i.e. an object X with a map I-->X where I is the unit for the monoidal structure). 2. It's the "symmetric monoidal category with I=0" freely generated by an object. 3. It's the monoidal category freely generated by an object X equipped with an involution s:X^2-->X^2 satisfying the braid relations and a morphism i:I-->X satisfying s.Xi=s.iX. Steve. On 4/12/08 8:11 PM, "Andrej Bauer" <andrej.bauer@andrej.com> wrote:
The category of finite sets and functions may be characterized (up to equivalence) as the category with finite coproducts freely generated from one object. Is there a similar nice characterization for the category of finite sets and _injective_ functions?
Best regards,
Andrej