From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Michael Shulman <shu...@sandiego.edu>
Cc: Homotopy Type Theory <homotopyt...@googlegroups.com>
Subject: Re: [HoTT] Identity versus equality
Date: Mon, 11 May 2020 19:27:28 +0200 [thread overview]
Message-ID: <20200511172728.GB16935@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <CAOvivQxPWO-BqgG8EqOBPXrQUOtyiBK4yMaDq_pC+s4gOwpdoA@mail.gmail.com>
> FWIW there is no trouble at all with "internal categories" in HoTT;
what I meant is that they are "evil" in the sense that they allow one
to speak about equality of objects
but if you do it in the simplicial sets model of HoTT then they are not quite
the same as categories internal to sSet
they are rather the unstraightenings of simplicially enriched cats
whose homobjects are all contractible
the contractible objects in sSet are much richer than the subobjects of 1
one should not forget that the logic of sSet when viewed at
homotopically is boolean whereas the traditional logic of sSet is not
at all
but I do understand that ordinary finite limit cats do live in sSet
via nerve
Thomas
next prev parent reply other threads:[~2020-05-11 17:27 UTC|newest]
Thread overview: 61+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-05-05 8:47 Ansten Mørch Klev
2020-05-06 16:02 ` [HoTT] " Joyal, André
2020-05-06 19:01 ` Steve Awodey
2020-05-06 19:18 ` Michael Shulman
2020-05-06 19:31 ` Steve Awodey
2020-05-06 20:30 ` Joyal, André
2020-05-06 22:52 ` Thorsten Altenkirch
2020-05-06 22:54 ` Thorsten Altenkirch
2020-05-06 23:29 ` Joyal, André
2020-05-07 6:11 ` Egbert Rijke
2020-05-07 6:58 ` Thorsten Altenkirch
2020-05-07 9:04 ` Ansten Mørch Klev
2020-05-07 10:09 ` Thomas Streicher
2020-05-07 16:13 ` Joyal, André
2020-05-07 21:41 ` David Roberts
2020-05-07 23:43 ` Joyal, André
2020-05-07 23:56 ` David Roberts
2020-05-08 6:40 ` Thomas Streicher
2020-05-08 21:06 ` Joyal, André
2020-05-08 23:44 ` Steve Awodey
2020-05-09 2:46 ` Joyal, André
2020-05-09 3:09 ` Jon Sterling
[not found] ` <CADZEZBY+3z6nrRwsx9p-HqYuTxAnwMUHv7JasHy8aoy1oaGPcw@mail.gmail.com>
2020-05-09 2:50 ` Steve Awodey
2020-05-09 8:28 ` Thomas Streicher
2020-05-09 15:53 ` Joyal, André
2020-05-09 18:43 ` Thomas Streicher
2020-05-09 20:18 ` Joyal, André
2020-05-09 21:27 ` Jon Sterling
2020-05-10 2:19 ` Joyal, André
2020-05-10 3:04 ` Jon Sterling
2020-05-10 9:09 ` Thomas Streicher
2020-05-10 11:59 ` Thorsten Altenkirch
2020-05-10 11:46 ` Thorsten Altenkirch
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:20 ` Nicolai Kraus
2020-05-10 14:34 ` Michael Shulman
2020-05-10 14:52 ` Nicolai Kraus
2020-05-10 15:16 ` Michael Shulman
2020-05-10 15:23 ` Nicolai Kraus
2020-05-10 16:13 ` Nicolai Kraus
2020-05-10 16:28 ` Michael Shulman
2020-05-10 18:18 ` Nicolai Kraus
2020-05-10 19:15 ` Thorsten Altenkirch
2020-05-10 19:20 ` Thorsten Altenkirch
2020-05-10 12:53 ` Ulrik Buchholtz
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:27 ` Nicolai Kraus
2020-05-10 15:35 ` Ulrik Buchholtz
2020-05-10 16:30 ` Michael Shulman
2020-05-10 18:56 ` Nicolai Kraus
2020-05-10 18:04 ` Joyal, André
2020-05-11 7:33 ` Thomas Streicher
2020-05-11 14:54 ` Joyal, André
2020-05-11 16:37 ` stre...
2020-05-11 16:42 ` Michael Shulman
2020-05-11 17:27 ` Thomas Streicher [this message]
2020-05-10 16:51 ` Nicolai Kraus
2020-05-10 18:57 ` Michael Shulman
2020-05-10 19:18 ` Nicolai Kraus
2020-05-10 20:22 ` Michael Shulman
2020-05-10 22:08 ` Joyal, André
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