A preprint of my paper "Totally distributive categories and injective toposes" is now available at http://arxiv.org/abs/1108.4032 This paper subsumes the content of talks that I gave in Halifax and Schenectady. An abstract is included below. Your comments are welcome. Regards, Rory Lucyshyn-Wright Abstract: We establish a connection between the totally distributive categories, studied by Marmolejo, Rosebrugh, and Wood, and the injective and quasi-injective Grothendieck toposes, studied by Johnstone and Joyal. We show that every quasi-injective topos is totally distributive and that every injective topos is lex totally distributive. As a partial converse, we show that every lex totally distributive category with a small dense generator is a quasi-injective topos. In view of work of Johnstone-Joyal relating injective and quasi-injective toposes to continuous categories, our results provide partial analogues of the dual equivalence between continuous dcpos and completely distributive lattices (Hoffmann, Lawson) and its restriction to continuous lattices (Banaschewski). [For admin and other information see: http://www.mta.ca/~cat-dist/ ]