Rig vs bimonoidal categories I was wondering if rig categories (as discussed here ncatlab: rig category for example), are the same thing as bimonoidal categories (as discussed here Bimonoidal Structure of Probability Monads
 for example).

The nlab page explicitly states that bimonoidal category is another name for rig categories. But in the paper you link, a bimonoidal structure is some structure which you can put on a monad, consisting of a monoidal and an opmonoidal structure which are compatible with each other (see section 3). These are entirely different concepts (there might be a connection since categories are just monads in the bicategory of spans, but I doubt that). In fact, the paper does not even mention "bimonoidal categories".
