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format=flowed; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable 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=20 course the notion of universal element, which comes from Yoneda.)=20 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= =20 > mailing list group from Macquarie University. > > Leave group:=20 > https://protect-au.mimecast.com/s/PLDmCNLJxkiLmR4lfmyv5q?domain=3Doutlook= .office365.com --MCBoundary=_12310302140440171 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=ISO-8859-1 I agree. In my first-year graduate course on category theory, a= fter 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 ent= ire theory
>of deterministic computation can be emulated within group theory. But<= BR> >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 putt= ing it
>into a fruit salad."
>
>Best to all,
>Robert Dawson
>
>
>
>----------
>
> You're receiving this message because you're a member of the Categorie= s
> mailing list group from Macquarie University.
>
> Leave group:
> https://outlook.office365.com/owa/categories@= mq.edu.au/groupsubscription.ashx?source=3DEscalatedMessage&action=3Dlea= ve&GuestId=3D623baca8-b6f6-4bcb-9e43-a41e17b7b8c8
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