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 I → X.
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 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.
Other articles related to "initial and terminal objects, initial, terminal object, object, objects":
... 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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