Re: Categories vis-a-vis Naturality

[ptj@maths.cam.ac.uk]

[-- Attachment #1: Type: text/plain, Size: 1505 bytes --]

I agree. In my first-year graduate course on category theory, after I've
shown that the three concepts `terminal object', `right adjoint' and
`limit' are all interdefinable, I jokingly add `You might say that
category-theorists have only ever had one good idea, and all we do
is to keep dressing it up in new clothes'. (The `one good idea' is of 
course the notion of universal element, which comes from Yoneda.) 
But the `dressing up in new clothes' does matter: the introduction of
(appropriate!) new concepts is an important aid to understanding. So
I think it is `selling category theory short' to describe it as `just'
the study of naturality.

Peter Johnstone

On Oct 29 2023, dawson wrote:

>I'm with David here.
>
>For some purposes it is genuinely useful to know that all categorical
>concepts can be reduced to "terminal object", or that the entire theory
>of deterministic computation can be emulated within group theory.  But
>that doesn't mean that this should always be done! Mathematics is all
>about knowing many ways to look at something, and choosing the right
>one(s).
>
>"Knowledge is knowing that a tomato is a fruit. Wisdom is not putting it
>into a fruit salad."
>
>Best to all,
>Robert Dawson
>
>
>
>----------
>
> You're receiving this message because you're a member of the Categories 
> mailing list group from Macquarie University.
>
> Leave group: 
> https://protect-au.mimecast.com/s/PLDmCNLJxkiLmR4lfmyv5q?domain=outlook.office365.com

[-- Attachment #2: Type: text/html, Size: 1963 bytes --]