 Category theory throws light on many mathematical structures. It has certainly been proposed as an alternative foundation for mathematics. Such generality inevitably runs into problems similar to those of comprehension in set theory; see, e.g., Hatcher 1982 (pp. 255–260). Hence there is the same possible application of inconsistent solutions. There is also an important collection of categorial structures, the toposes, which support open set logic in exact parallel to the way sets support Boolean logic. This has been taken by many to be a vindication of the foundational point of view of mathematical intuitionism. However, it can be proved that that toposes support closed set logic as readily as they support open set logic, to date the only category-theoretic semantics for a paraconsistent logic. This should not be viewed as an objection to intuitionism, however, so much as an argument that inconsistent theories are equally reasonable as items of mathematical study. See Mortensen (1995 Chap 11, co-author Lavers). This position has now been taken up, extended and ably defended by Estrada-González (2010, 2015a, 2015b). The same author (2016) undertakes to provide a category-theoretic description of trivial theories, with the aim of showing that triviality is not such an uninteresting feature for mathematical theories to have. The present author remains unconvinced, since a trivial theory is surely useless for mathematical calculation; but the ingenuity of the arguments must be conceded.