ABSTRACT
An object X in a category C is called initial (respectively, terminal) if HomCpX,Y q (respectively, HomCpY,Xq) is a singleton for all Y P ObpCq. An object X is a zero object if it is both an initial and a terminal object. Initial, terminal, and zero objects are unique up to isomorphisms. We will say that a category C is pointed if a zero object exists. We will denote the zero object of a pointed category by 0.
