From: Michael Barr <barr@barrs.org>
To: categories@mta.ca
Subject: Re: Why binary products are ordered
Date: Thu, 8 Feb 2001 12:44:59 -0500 (EST) [thread overview]
Message-ID: <Pine.LNX.4.10.10102081243440.21476-100000@triples.math.mcgill.ca> (raw)
In-Reply-To: <200102080117.RAA13130@coraki.Stanford.EDU>
As I said in an earlier post, the whole thing is a figment of the linear
way we write (and speak, for that matter). Products are over unordered
sets and any ordering is purely irrelevant.
On Wed, 7 Feb 2001, Vaughan Pratt wrote:
...
> I confess to some confusion as to what Charles is insisting is inevitable
> here. A binary product in C is a limit of a diagram 1+1->C (1+1 the
> two-object discrete category), and 1+1 has two automorphisms. This much
> and its mathematical consequences are surely inevitable.
>
> But woven into Charles' argument is what Bill has called the "totally
> arbitrary singleton operation of Peano." It appears implicitly at the
> beginning when Charles names the projections, and then (after an indirect
> reference to the automorphisms of the binary product) more explicitly
> when he collects the names as a set.
>
> Surely anyone insisting on names like 1 and 2 or red and blue for the
> projections of binary product is backsliding into the ZFvN tarpit of
> spurious rigidified membership. If this backsliding really is inevitable
> as Charles seems to be saying, how does one reconcile this with Bill's
> view of "rigidified membership" as "mathematically spurious"?
>
> Must mathematics accept the spurious, in this or any other case?
>
> Vaughan
>
next prev parent reply other threads:[~2001-02-08 17:44 UTC|newest]
Thread overview: 12+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-01-29 18:18 Charles Wells
2001-02-08 1:17 ` Vaughan Pratt
2001-02-08 9:14 ` Colin McLarty
2001-02-11 19:40 ` zdiskin
2001-02-08 17:44 ` Michael Barr [this message]
2001-02-11 1:54 ` zdiskin
2001-02-13 18:17 ` Nick Rossiter
2001-02-11 0:10 ` Dusko Pavlovic
2001-02-11 17:24 ` Singleton as arbitrary Colin McLarty
2001-02-13 4:34 ` Dusko Pavlovic
2001-01-30 16:43 Why binary products are ordered S.J.Vickers
[not found] ` <20010131135719.A5824@kamiak.eecs.wsu.edu>
2001-02-01 11:10 ` S Vickers
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