Re: terminology in definitions of limits

[Vaughan Pratt <pratt@cs.stanford.edu>]

Colin McLarty wrote:
> I often call them "test objects" in talking with students (by analogy
> with "test particles" in General Relativity).  I don't think I have ever
> done it in print.  But I did use "T" as the typical name of such an
> object in my book.
>
> I am curious to know what others think.

 From a game-theoretic standpoint one can be either taking the test or
administering it.  Both sides call it the test, showing that the name is
stable under perp (change of team).

However that's not to say that "test" gives a helpful perspective in
either case.  A right adjoint defined by its adjunction is simply a
specification of *all* homsets to it, and dually, in the case of left
adjoints, of all the homsets from it.  What you're calling a "test"
object there is for me merely the variable being universally quantified
over in the definition of "all."

Whether a student is going to find it helpful thinking of a universally
quantified variable as a "test object" is going to be less a question of
what the student thinks about that perspective than what the teacher
thinks about it and whether they can convey their point of view.  The
mathematically talented student who immediately sees it is merely being
universally quantified over may be more puzzled than helped.

But then how many of us are so lucky as to have a significant number of
mathematically talented students in our classes?

Vaughan