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

[Ben Franksen]

Albert Y. C. Lai wrote:
> On 2015-03-08 12:11 PM, Eric wrote:
>> In some sense it's a canonical instance of Foo; we could trivially
>> write a universal
>>
>> > toFoo' :: Foo f => f -> Foo'
>>
>> function.
> 
> 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.

Cheers
Ben