11 Mar
2015
11 Mar
'15
2:22 p.m.
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.