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boundary="_000_70CE06D701EB4F51A0BA6285601D8495mqeduau_" MIME-Version: 1.0 X-OriginatorOrg: mq.edu.au --_000_70CE06D701EB4F51A0BA6285601D8495mqeduau_ Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D "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? =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D 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 mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --_000_70CE06D701EB4F51A0BA6285601D8495mqeduau_ Content-Type: text/html; charset="us-ascii" Content-ID: <0B353140444A274985E3F85E34A1B75F@ausprd01.prod.outlook.com> Content-Transfer-Encoding: quoted-printable
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
 "Yoneda showed that maps in any category can be
represented as natural transformations" (Lawvere & Schanuel,<= /div>
Conceptual Mathematics, p. 378). Isn't this reason enough to think of<= /div>
category theory as the theory of naturality?
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

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


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 cat= egory
theory was to define natural transformation. That required functor, an= d
that required category.

Ross 
 
 
You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message.
 
View group files   |   Leav= e group   |&n= bsp;  Learn more about Microsoft 365 Groups
 
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