[Haskell-cafe] Is there a name for this?

[Albert Y. C. Lai]

On 2015-03-09 11:26 AM, Ben Franksen wrote:
> Albert Y. C. Lai wrote:
>> Choose one:
>>
>> Foo' is a free Foo
>>
>> Foo' is a limit of the diagram of Foo
>>
>> Foo' is a terminal object of the [sub]category of Foo
>
> Interesting. Is the last variant how "free <whatever>" is usually defined?
> Or is it a coincidence that the two, well, coincide here? I remember I have
> seen other definitions that looked a lot less easy to understand.

I have not checked, and too lazy to.

The usual "free" is the less-easy-to-understand one: you need a 
forgetful functor, then you need its left adjoint, and you call it your 
free functor. Then the target objects hit by the free functor are the 
free things.