In Sets+Injective functions (Inj?) the disjoint sum A+B obeys a universal property which is slightly more restricted than coproduct: given two maps A ---> C <--- B such that their pullback is empty, then there exists a unique A+B ----> C with the usual coproduct- filler property. So I guess that if you look for the free category with one generator object, pullbacks, initial object and a bifunctor+natural transformations with that universal property, you will get FInj, but that has to be ascertained. Hope that helps, François On 4 déc. 08, at 10:11, Andrej Bauer 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