Re: only_marketing_?

[Vaughan Pratt <pratt@cs.stanford.edu>]

Formulating the *future *with category theory?  My understanding is that
the *present *is already formulated less with set theory than with category
theory, at least its morphisms under composition, and has been for a long
time.

In 1969 Jack Schwartz introduced the programming language SETL based on set
theory.  However programmers found it much easier to write programs as
functions composed from simpler functions than to implement them with sets
based on membership, and SETL never caught on.

There have also been sporadic attempts to introduce set theory into K-12
mathematics, under such rubrics as "New maths", starting with the
operations of union and intersection, but these have not caught on either.

Category theory is an abstract formulation of functions taking composition
as the primitive operation.  Functions are in wide use in both mathematics
and software.  Whenever a function calls another function from within it,
that's composition.

In recent years I've been promoting a viewpoint of algebra that emphasizes
the associativity of composition as the root of not just algebra but
bialgebra in the sense of typed Chu spaces.  The defining properties of
both homomorphisms and Chu transforms follow from associativity.  My most
recent talk on this was at FMCS in June, the "ten" slides are here
<http://boole.stanford.edu/pub/fmcs.pdf>.  (They're less cryptic when the
speaker is there to explain them, especially with an audience of only one
or two and with no time pressure.)

One might call this "category light" by virtue of working in the *class*
CAT, i.e. just categories, no functors etc.  By Yoneda (unintended pun
there, it's actually "biYoneda")  the functors are there, they're just
"under the hood".  Just as you only need to know what sort of engine is in
the car you're driving if you have to service it, you only need to know
about functors, natural transformations, etc. when you become a "category
mechanic" so to speak.

Sets are automatic because they arise wherever morphisms gather together in
those spaces we call homsets.

Vaughan

On Sun, Aug 11, 2019 at 7:20 AM Patrik Eklund <peklund@cs.umu.se> wrote:

> It's an article that names the company Risk Group LLC (with John Baez as
> co-founder).
>
> The website of Risk Group has 'warfare' as the first menu item in the
> menu row. Under other menus there is AI and such related things that
> industry more in general is interested in. There are relations to health
> care solutions etc, so the ambition is broad.
>
> "Is it pure marketing?" I don't know about 'pure', but it looks like
> marketing, at least partly, and why not? I for one wish Risk Group as a
> company all the best. If category theory becomes more in focus in
> applications serving the public and private sectors in general, also as
> promoted by Risk Group LLC, this is fine.
>
> Possible relations to military application I wouldn't personally
> support, but that's my personal choice. I'm a European, and work e.g.
> with health care aspects as related also to the European Commission.
>
> All the best,
>
> Patrik
>
> www.glioc.com
>
>
>
> On 2019-08-06 17:37, Eduardo J. Dubuc wrote:
>> Hi, I will like to hear opinions of members of this list about the
>> following link:
>>
>>
> https://www.forbes.com/sites/cognitiveworld/2019/07/29/the-future-will-be-formulated-using-category-theory/
>>
>> Is it pure marketing ?
>>
>> Is it serious ?
>>
>> The points in this post can attire more funds to category theory
>> research in general ?
>>
>> The point in this post will absorb for fake category theory research
>> the
>> existing funds in detriment to serious category theory research ?
>>
>> etc etc
>>
>> eduardo dubuc
>>
>>
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
>

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<div dir=3D"ltr"><div>Formulating the <i>future </i>with category theory?=
=C2=A0 My understanding is that the <i>present </i>is already formulated le=
ss with set theory than with category theory, at least its morphisms under =
composition, and has been for a long time.<br></div><div><br></div><div>In =
1969 Jack Schwartz introduced the programming language SETL based on set th=
eory.=C2=A0 However programmers found it much easier to write programs as f=
unctions composed from simpler functions than to implement them with sets b=
ased on membership, and SETL never caught on.</div><div><br></div><div>Ther=
e have also been sporadic attempts to introduce set theory into K-12 mathem=
atics, under such rubrics as &quot;New maths&quot;, starting with the opera=
tions of union and intersection, but these have not caught on either.<br></=
div><div><br></div><div>Category theory is an abstract formulation of funct=
ions taking composition as the primitive operation.=C2=A0 Functions are in =
wide use in both mathematics and software.=C2=A0 Whenever a function calls =
another function from within it, that&#39;s composition.<br></div><div><br>=
</div><div>In recent years I&#39;ve been promoting a viewpoint of algebra t=
hat emphasizes the associativity of composition as the root of not just alg=
ebra but bialgebra in the sense of typed Chu spaces.=C2=A0 The defining pro=
perties of both homomorphisms and Chu transforms follow from associativity.=
=C2=A0 My most recent talk on this was at FMCS in June, <a href=3D"http://b=
oole.stanford.edu/pub/fmcs.pdf">the &quot;ten&quot; slides are here</a>.=C2=
=A0 (They&#39;re less cryptic when the speaker is there to explain them, es=
pecially with an audience of only one or two and with no time pressure.)<br=
></div><div><br></div><div> One might call this &quot;category light&quot; =
by virtue of working in the <i>class</i> CAT, i.e. just categories, no func=
tors etc.=C2=A0 By Yoneda (unintended pun there, it&#39;s actually &quot;bi=
Yoneda&quot;)=C2=A0 the functors are there, they&#39;re just &quot;under th=
e hood&quot;.=C2=A0 Just as you only need to know what sort of engine is in=
  the car you&#39;re driving if you have to service it, you only need to kno=
w about functors, natural transformations, etc. when you become a &quot;cat=
egory mechanic&quot; so to speak.</div><div><br></div><div>Sets are automat=
ic because they arise wherever morphisms gather together in those spaces we=
  call homsets.</div><div><br></div><div>Vaughan<br></div></div><br><div cla=
ss=3D"gmail_quote"><div dir=3D"ltr" class=3D"gmail_attr">On Sun, Aug 11, 20=
19 at 7:20 AM Patrik Eklund &lt;<a href=3D"mailto:peklund@cs.umu.se">peklun=
d@cs.umu.se</a>&gt; wrote:<br></div><blockquote class=3D"gmail_quote" style=
=3D"margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding=
-left:1ex">It&#39;s an article that names the company Risk Group LLC (with =
John Baez as<br>
co-founder).<br>
<br>
The website of Risk Group has &#39;warfare&#39; as the first menu item in t=
he<br>
menu row. Under other menus there is AI and such related things that<br>
industry more in general is interested in. There are relations to health<br=
>
care solutions etc, so the ambition is broad.<br>
<br>
&quot;Is it pure marketing?&quot; I don&#39;t know about &#39;pure&#39;, bu=
t it looks like<br>
marketing, at least partly, and why not? I for one wish Risk Group as a<br>
company all the best. If category theory becomes more in focus in<br>
applications serving the public and private sectors in general, also as<br>
promoted by Risk Group LLC, this is fine.<br>
<br>
Possible relations to military application I wouldn&#39;t personally<br>
support, but that&#39;s my personal choice. I&#39;m a European, and work e.=
g.<br>
with health care aspects as related also to the European Commission.<br>
<br>
All the best,<br>
<br>
Patrik<br>
<br>
<a href=3D"http://www.glioc.com" rel=3D"noreferrer" target=3D"_blank">www.g=
lioc.com</a><br>
<br>
<br>
<br>
On 2019-08-06 17:37, Eduardo J. Dubuc wrote:<br>
&gt; Hi, I will like to hear opinions of members of this list about the<br>
&gt; following link:<br>
&gt;<br>
&gt; <a href=3D"https://www.forbes.com/sites/cognitiveworld/2019/07/29/the-=
future-will-be-formulated-using-category-theory/" rel=3D"noreferrer" target=
=3D"_blank">https://www.forbes.com/sites/cognitiveworld/2019/07/29/the-futu=
re-will-be-formulated-using-category-theory/</a><br>
&gt;<br>
&gt; Is it pure marketing ?<br>
&gt;<br>
&gt; Is it serious ?<br>
&gt;<br>
&gt; The points in this post can attire more funds to category theory<br>
&gt; research in general ?<br>
&gt;<br>
&gt; The point in this post will absorb for fake category theory research<b=
r>
&gt; the<br>
&gt; existing funds in detriment to serious category theory research ?<br>
&gt;<br>
&gt; etc etc<br>
&gt;<br>
&gt; eduardo dubuc<br>
&gt;<br>
&gt;<br>
<br>
<br>
[For admin and other information see: <a href=3D"http://www.mta.ca/~cat-dis=
t/" rel=3D"noreferrer" target=3D"_blank">http://www.mta.ca/~cat-dist/</a> ]=
<br>
</blockquote></div>

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[For admin and other information see: http://www.mta.ca/~cat-dist/ ]