The extensive reflection of a distributive category

Steve Lack – 2 July 1997

I described an explicit construction of the left biadjoint to the inclusion in the 2-category of distributive categories of the full sub-2-category comprising those distributive categories which are in fact extensive. Given a distributive category A, an object of the extensive reflection of A is an arrow a:A-->1+1 of A, and an arrow from a:A-->1+1 to b:B-->1+1 is an arrow f:A-->B+1 of A satisfying a certain condition. The details are in my thesis The algebra of distributive and extensive categories. The description is quite simple, but not particularly conceptual, and I then gave the beginnings of an attempt to give a more conceptual explanation; this lead to a discussion of the so-called ``strong'' monads.