Here is another contribution to the baptism of "stable functors". When a functor F represents a datatype construction, such as lists, trees or matrices, then it typically preserves pullbacks (in fact, all connected limits) and when applied to the terminal object 1 yields the "basic shape" F1 whose "elements" are the shapes of general data. For example, the list functor applied to 1 is a NNO since the shape of a list is its length. In this setting it is attractive to call pullback-preserving functors "shapely". Similarly, the natural transformations representing the generic operations on the datatypes (e.g. the appending of lists or flattening of trees) often have the property that the commuting squares arising in their definition are actually pullbacks. Such natural transformations are commonly known as cartesian natural transformations, but in this setting could also be called "shapely natural transformations". Thus there is a 2-category consisting of categories with finite (connected?) limits, shapely functors and shapely natural transformations, which is convenient for studying the general theory of datatypes. Barry Jay =====================================================================