My preprint "Totally distributive toposes" (http://arxiv.org/abs/1108.4032) has been updated to include an extended result, namely that the lex totally distributive categories with a small set of generators are exactly the injective Grothendieck toposes. Regards, Rory Lucyshyn-Wright Abstract: A locally small category E is totally distributive (as defined by Rosebrugh-Wood) if there exists a string of adjoint functors t -| c -| y, where y : E --> E^ is the Yoneda embedding. Saying that E is lex totally distributive if, moreover, the left adjoint t preserves finite limits, we show that the lex totally distributive categories with a small set of generators are exactly the injective Grothendieck toposes, studied by Johnstone and Joyal. We characterize the totally distributive categories with a small set of generators as exactly the essential subtoposes of presheaf toposes, studied by Kelly-Lawvere and Kennett-Riehl-Roy-Zaks. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]