Initial object

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

An initial object of a category 𝕮 is an object 𝑰 in 𝕮 such that for every object 𝑿 in 𝕮, there exists precisely 1 morphism from 𝑰 to 𝑿, 𝓜 : 𝑰 → 𝑿.

Initial objects are also called coterminal objects or universal 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 strict initial object I is one for which every morphism into I is an isomorphism.

A is the initial object:

     B
     ↑
D <- A -> C
     ↓
     D

• The empty set is the unique initial object in the category Set

• There are no zero objects in the category Set