  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.
