 Some have thought that the fact that NFU combines a universal set and other big structures with mathematical fluency in treating these structures might make it a suitable medium for category theory. Although we have some inclination to be partial to this class of set theories, we note that there are strong counterarguments to this view. It is true that there are big categories, such as the category of all sets (as objects) and functions (as the morphisms between them), the category of all topological spaces and homeomorphism, and even the category of all categories and functors. However, the category of all sets and functions, for example, while it is a set, is not “cartesian closed” (a technical property which this category is expected to have): see McLarty 1992. Moreover, if one restricts to the s.c. sets and functions, one obtains a cartesian closed category, which is much more closely analogous to the category of all sets and functions over ZFC—and shares with it the disadvantage of being a proper class! Contemplation of the models only confirms the impression that the correct analogue of the proper class category of sets and functions in ZFC is the proper class category of s.c. sets and functions in NFU! There may be some applications for the big set categories in NFU, but they are not likely to prove to be as useful as some have optimistically suggested. See Feferman 2006 for an extensive discussion.