 Category theory was first developed, against the background of these developments, as a unifying framework for the study of the relations between different mathematical structures (cf.  Landry &amp; Marquis 2005, Marquis 2009). Different types of mappings were introduced for this task. One type involves the morphisms between the objects of the same category, e.g., group homomorphisms in the category of groups, or linear maps in the category of vector spaces. Another important type of mappings are “functors” between different categories. (Roughly, a functor between two categories is a mapping of objects to objects and arrows to arrows that preserves the categorical properties in question.) It is such functors that are the central tools in category-theory for comparing the objects of different mathematical categories, and thus, to “relate structures of different kinds” (Awodey 1996).  As such, they are central to categorical structuralism.