Initial and Terminal Objects

Initial And Terminal Objects

In category theory, an abstract 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 IX.

The 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 XT. 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.

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Other articles related to "initial and terminal objects, initial, terminal object, object, objects":

Initial And Terminal Objects - Properties - Other Properties
... The endomorphism monoid of an initial or terminal object I is trivial End(I) = Hom(I,I) = { idI } ... If a category C has a zero object 0 then for any pair of objects X and Y in C the unique composition X → 0 → Y is a zero morphism from X to Y ...

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