Technically, yes, they'd be fine together but a 10 gallon is too small for a group of corys. Some here even suggest that a 10 gallon would be too small for even Pygmy corys because they need to be in a large group.
In the tank that you have there are not any corys that can live and be happy in that tank, all of the corys are happiest in a group of 6 or more and most types get relatively large for the size they are sold at pet stores.
thanks for all of the replies...they reason i'm asking is that i recently had my first batch of guppy fry and was going to put some of them in a separate tank, and thought some cory cats would be cool to have since i don't have any of those. i'm not completely sure of the tank size...its one of those Walmart specials...maybe its a 15? not sure.