Re: Categories and functors, query

[Toby Bartels <toby+categories@ugcs.caltech.edu>]

Dana Scott wrote in part:

>But, as
>everyone knows, it is not the definition of a category that
>is the key part, but seeing that functors and natural
>transformations are interesting.

Indeed, the notion of natural isomorphism (or canonical isomorphism)
should be available already to groupoid theorists before 1945.
To what extent did they know about functors and natural isomorphisms,
and to what extent did Saunders & Mac Lane have to tell them?
Or, pace Walter's remarks, did they know about the ~small~ ones
but not have the guts to apply them to large classes of strucures?

It's been said before that the real insight of category theory
--as something more general than groupoids, monoids, and posets--
is the notion of adjoint functors (including limits, etc).
I'm inclined to agree, so I'm interested in why and whether
groupoid theorists thought of (and applied) that which they ~did~ have.


--Toby