# Terminal object

<https://en.wikipedia.org/wiki/Initial_and_terminal_objects>

The dual notion of an initial object is that of a terminal object (also called terminal element):

`T` is a terminal object, if for every object `X` in 𝕮 there exists exactly one morphism `X → T`.

*Terminal objects* are also called *final objects*.

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.

A is the terminal object:

```
     B
     ↓
D -> A <- C
     ↑
     D
```

* every singleton set is a terminal object in the category Set
* there are no zero objects in the category Set


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