Category theory reveals how different kinds of structures are related to one another. For instance, in algebraic topology, topological spaces are related to groups (and modules, rings, etc.) in various ways (such as homology, cohomology, homotopy, K-theory). As noted above, groups with group homomorphisms constitute a category. Eilenberg & Mac Lane invented category theory precisely in order to clarify and compare these connections. What matters are the morphisms between categories, given by functors. Informally, morphisms are structure-preserving maps between categories.