# 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]}