**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":

**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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“Capital is a result of labor, and is used by labor to assist it in further production. Labor is the active and *initial* force, and labor is therefore the employer of capital.”

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“All sin tends to be addictive, and the *terminal* point of addiction is what is called damnation.”

—W.H. (Wystan Hugh)