From: categories <cat-dist@mta.ca>
To: categories <categories@mta.ca>
Subject: Re: Is cut semantical?
Date: Wed, 27 Aug 1997 10:31:46 -0300 (ADT) [thread overview]
Message-ID: <Pine.OSF.3.90.970827103138.18149B-100000@mailserv.mta.ca> (raw)
Date: Tue, 26 Aug 1997 09:25:31 -0700
From: Vaughan R. Pratt <pratt@cs.Stanford.EDU>
From: Michael Barr <barr@triples.math.mcgill.ca>
I should clarify. Proofs with cuts correspond to composable paths.
If you like, to proofs in the graph (or free category) of a category.
Yes, the free thing on the syntax you're trying to model usually does
the job, e.g. the Lindenbaum algebra. But is there any mathematical
object arising in nature that works like proofs with cut, the way
natural transformations do for cut-free proofs? It is somewhat magical
that natural transformations match proofs in this way when they do, and
reassuring when they don't: they're letting you know they're alive and
require maintenance, unlike free things which are dead and therefore
maintenance-free.
Vaughan
next reply other threads:[~1997-08-27 13:31 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
1997-08-27 13:31 categories [this message]
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1997-08-26 15:18 categories
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