Extensive category

In mathematics, an extensive category is a category "C" with finite coproducts that are disjoint and well-behaved with respect to pullbacks. Equivalently, "C" is extensive if the coproduct functor from the product of the slice categories "C"/"X" × "C"/"Y" to the slice category "C"/("X" + "Y") is an equivalence of categories for all objects "X" and "Y" of "C".
Examples.
The categories Set and Top of sets and topological spaces, respectively, are extensive categories. More generally, the category of presheaves on any small category is extensive.
The category CRing"op" of affine schemes is extensive.