A simplified definition of logically distributive categories
  In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the definition of logically distributive category can be simplified by dropping two requirements, the one saying that product must distribute over sum, and the one saying that product must distribute over existential quantification. 
Marco Benini
math.CT