category theory, a branch of
mathematics, an initial object of a
category C is an object I in C such that for every object X in C, there exists precisely one
morphism I → X.
dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
If an object is both initial and terminal, it is called a zero object or null object. A pointed category is one with a zero object.
strict initial object I is one for which every morphism into I is an