From: Ross Street <ross.street@mq.edu.au>
To: JS Lemay <js.lemay@mq.edu.au>
Cc: Categories mailing list <categories@mq.edu.au>,
posinavrayudu <posinavrayudu@gmail.com>
Subject: Re: Categories vis-a-vis Naturality
Date: Sun, 29 Oct 2023 06:31:43 +0000 [thread overview]
Message-ID: <70CE06D7-01EB-4F51-A0BA-6285601D8495@mq.edu.au> (raw)
In-Reply-To: <ME2PR01MB3122A47E3DA7719BC33CF4B1CDA3A@ME2PR01MB3122.ausprd01.prod.outlook.com>
[-- Attachment #1: Type: text/plain, Size: 1464 bytes --]
================================================
"Yoneda showed that maps in any category can be
represented as natural transformations" (Lawvere & Schanuel,
Conceptual Mathematics, p. 378). Isn't this reason enough to think of
category theory as the theory of naturality?
================================================
That would be like saying group theory is the theory of permutations
(because of the Cayley theorem).
Perhaps my little colloquium talk entitled
``The natural transformation in mathematics''
at
http://science.mq.edu.au/~street/MathCollMar2017_h.pdf
would be of some interest in this connexion. I am sure lots of us have
given similar talks. The goal of the paper considered the first in category
theory was to define natural transformation. That required functor, and
that required category.
Ross
You're receiving this message because you're a member of the Categories mailing list group from Macquarie University. To take part in this conversation, reply all to this message.
View group files<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=files&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b> | Leave group<https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.ashx?source=EscalatedMessage&action=leave&GuestId=4eb9b40c-9b3a-48a5-9781-836e5a171e8b> | Learn more about Microsoft 365 Groups<https://aka.ms/o365g>
[-- Attachment #2: Type: text/html, Size: 3771 bytes --]
next prev parent reply other threads:[~2023-10-29 9:14 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2023-10-23 5:39 Welcome to the new Categories mailing list JS Lemay
2023-10-23 8:26 ` JS Lemay
[not found] ` <CAL+Rf9fA9UXuN3wgyg3DYXOCryh=RY0Weu40rRf6Hkxd8n1BRw@mail.gmail.com>
2023-10-28 20:46 ` Categories vis-a-vis Naturality JS Lemay
[not found] ` <CABTYDMHwtDbb6c1zgyAELzSSg=-xf20RTSJ6JLOpRj22vxmqJg@mail.gmail.com>
[not found] ` <F761733C-9F28-4C2B-B445-024DFE3C2BA8@mq.edu.au>
[not found] ` <CABTYDME5rLeodDD_qZ5qpFyUyd9=aoxg2mo+MK+vTEHxmaqc=g@mail.gmail.com>
2023-10-28 21:37 ` Johnathon Taylor
2023-10-29 6:31 ` Ross Street [this message]
2023-10-29 10:12 ` Posina Venkata Rayudu
2023-10-29 18:18 ` Johnathon Taylor
2023-10-29 19:33 ` Posina Venkata Rayudu
2023-10-29 19:50 ` Johnathon Taylor
2023-10-30 0:54 ` Vaughan Pratt
2023-10-29 21:14 ` David Roberts
2023-10-29 22:38 ` dawson
2023-10-30 7:17 ` Patrik Eklund
2023-10-30 10:40 ` ptj
2023-10-30 7:08 ` Patrik Eklund
2023-10-29 13:00 ` [EXT] " Bob Coecke
2023-10-29 13:50 ` Posina Venkata Rayudu
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=70CE06D7-01EB-4F51-A0BA-6285601D8495@mq.edu.au \
--to=ross.street@mq.edu.au \
--cc=categories@mq.edu.au \
--cc=js.lemay@mq.edu.au \
--cc=posinavrayudu@gmail.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).