Dualizing comma categories

Hi, A comma category is a comma object in the 2-category Cat of categories and functors. And a comma object is defined by a universal property. Now, one can dualize the notion of comma object by turning around the 1-cells and/or 2-cells in its definition. My question is: when we instantiate those dualized definitions to Cat, what do we obtain? In other words, what is a "co-comma category"? For example, since the product of two categories is a special case of comma category, I would expect that the coproduct of two categories is a special case of "co-comma category". Thanks! [For admin and other information see: http://www.mta.ca/~cat-dist/ ]