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.[1]

The categories Set and Top of sets and topological spaces, respectively, are extensive categories.[2] More generally, the category of presheaves on any small category is extensive.[2]