In algebraic topology, the pushforward of a continuous function : between two topological spaces is a homomorphism between the homology groups for . Homology is a functor which converts a topological space into a sequence of homology groups . (Often, the collection of all such groups is referred to using the notation ; this collection has the structure of a graded ring.) In any category, a functor must induce a corresponding morphism. The pushforward is the morphism corresponding to the homology functor.