ABSTRACT
Functors provide us the association of the properties of the arrows of their source category with those of the arrows in their target category. There can be universal associations such as these. Such universal associations are important to the analysis of the structures forming categories. Arrows and objects in categories may display some special associations in relation to functors connecting them. Such an association can be that of a source in the domain category of a functor with a source in the codomain category of that functor. For category theory, such functor-related properties of arrows and objects are obviously important for the analysis of the relationships of various categories. This chapter presents notions of a universal coassociate and a universal coarrow, which are dual to those of a universal associate and a universal arrow, respectively. A co-reflection arrow is then an example of a universal coarrow.
