From: Mike Stay <metaweta@gmail.com>
To: Baruch Garcia <baruchgarcia@gmail.com>
Cc: categories <categories@mta.ca>
Subject: Re: The use-mention distinction and category theory
Date: Tue, 5 Sep 2017 11:36:45 -0600 [thread overview]
Message-ID: <E1dpbiW-0002Vc-7B@mlist.mta.ca> (raw)
In-Reply-To: <E1dp1ks-0001aL-0Q@mlist.mta.ca>
On Sun, Sep 3, 2017 at 1:19 PM, Baruch Garcia <baruchgarcia@gmail.com> wrote:
> Hello,
>
> I was wondering if someone of the categories list could answer this
> question:
>
> In Godel's/Tarski's theorem and the Halting problem, the use-mention
> distinction (e.g. Boston is populous, but "Boston" is disyllabic) is
> essential. Is there an analog to the use-mention distinction in category
> theory or is the use-mention distinction just its own principle independent
> of category theory?
There's something like a distinction between use and mention in a
symmetric monoidal closed category. Given a morphism f:X -> Y,
there's the "name" of the function curry(f):I -> X -o Y, where I is
the monoidal unit and -o is the internal hom. The evaluation morphism
takes a value g of type X -o Y and a value x of type X and returns
uncurry(g)(x).
--
Mike Stay - metaweta@gmail.com
http://www.cs.auckland.ac.nz/~mike
http://reperiendi.wordpress.com
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2017-09-05 17:36 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-09-03 19:19 Baruch Garcia
2017-09-05 5:46 ` Patrik Eklund
2017-09-05 17:36 ` Mike Stay [this message]
2017-09-26 17:00 ` Gershom B
[not found] ` <CAM8RHpFX-L8TWmfef71v_NgH4wvtmrp+3GuQrUK4qCNV8bZ5Ug@mail.gmail.com>
2017-09-26 19:17 ` Baruch Garcia
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