From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Sergey Goncharov <sergey.goncharov@fau.de>
Cc: categories@mta.ca
Subject: Re: Predicativity in Categories
Date: Thu, 1 Dec 2016 15:55:10 +0100 [thread overview]
Message-ID: <E1cCWHd-00029Q-Pv@mlist.mta.ca> (raw)
In-Reply-To: <E1cBLlJ-0008KG-Ij@mlist.mta.ca>
Categorical Logic is such a versatile tool that it allows to give an
account uf both impredicative and predicatives systems.
A topos is a categorical account to higher order logic and thus
impredicative. A logos (Freyd) gives an account of intuit. first order
logic and thus is "predicative". A locally cartesian closed category
(after splitting) is a model of Martin-Loef type theory. That is
predicative. Both predicative and impredicative universes can be
defined categorically within lcc's. This was done is the second half
of the 1980s by many people (including myself).
Whether category theory itself is "impredicative" however is an
ill-posed question in my eyes.
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2016-12-01 14:55 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-11-27 18:53 Sergey Goncharov
2016-11-30 11:01 ` Steve Vickers
2016-12-01 16:05 ` Sergey Goncharov
2016-12-01 14:55 ` Thomas Streicher [this message]
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