From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Michael Shulman <shulman@sandiego.edu>
Cc: Thorsten Altenkirch <Thorsten.Altenkirch@nottingham.ac.uk>,
Ulrik Buchholtz <ulrikbuchholtz@gmail.com>,
homotopytypetheory@googlegroups.com
Subject: Re: [HoTT] Re: Precategories, Categories and Univalent categories
Date: Fri, 9 Nov 2018 12:56:53 +0100 [thread overview]
Message-ID: <20181109115653.GA7030@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <CAOvivQyd+xEe4AHAFM02YrjSQs2sTumCXOMY=d4FdrLaAkQjdw@mail.gmail.com>
Benedikt and Peter essentially employ an old result of Benabou saying that
functors to BB correspond normalized lax functor from BB^op to Dist,
the bicategory of distributors. But, obviously, the forward direction requires
equality of objects.
Accordingly, they can't express composition of functors in terms of
the associated normalized lax functors.
Even classically, going from fibrations to indexed categories involves
choice. But going from functors to normalized lax functors just
requires equality of objects.
Thomas
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next prev parent reply other threads:[~2018-11-09 11:56 UTC|newest]
Thread overview: 46+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-11-07 10:03 [HoTT] " Ali Caglayan
2018-11-07 10:31 ` [HoTT] " Paolo Capriotti
2018-11-07 10:35 ` Ulrik Buchholtz
2018-11-07 10:37 ` Ulrik Buchholtz
2018-11-07 11:09 ` Peter LeFanu Lumsdaine
2018-11-07 11:43 ` Ulrik Buchholtz
2018-11-07 11:50 ` Erik Palmgren
2018-11-07 11:51 ` Ulrik Buchholtz
2018-11-07 12:03 ` Erik Palmgren
2018-11-07 12:21 ` Martín Hötzel Escardó
2018-11-07 13:00 ` Erik Palmgren
2018-11-07 13:02 ` Bas Spitters
2018-11-07 13:47 ` Ali Caglayan
2018-11-07 13:53 ` Thomas Streicher
2018-11-07 14:05 ` Thorsten Altenkirch
2018-11-07 13:58 ` Thorsten Altenkirch
2018-11-07 14:14 ` Ulrik Buchholtz
2018-11-07 14:27 ` Peter LeFanu Lumsdaine
[not found] ` <CAOvivQyG1q9=3YoS8hX3bRQK0yi+mpBnJu+rqb3oon0uPLpZ4A@mail.gmail.com>
2018-11-07 20:01 ` Michael Shulman
2018-11-08 21:37 ` Martín Hötzel Escardó
2018-11-08 21:43 ` Michael Shulman
2018-11-09 4:43 ` Andrew Polonsky
2018-11-09 10:18 ` Ulrik Buchholtz
2018-11-09 10:57 ` Paolo Capriotti
2018-11-07 14:31 ` Thorsten Altenkirch
2018-11-07 14:05 ` Peter LeFanu Lumsdaine
2018-11-07 14:28 ` Ulrik Buchholtz
2018-11-07 15:35 ` Thomas Streicher
2018-11-07 16:54 ` Thorsten Altenkirch
2018-11-07 16:56 ` Thorsten Altenkirch
2018-11-07 17:31 ` Eric Finster
2018-11-08 11:58 ` Thomas Streicher
2018-11-08 12:23 ` [HoTT] " Emily Riehl
2018-11-08 12:28 ` Emily Riehl
2018-11-08 14:01 ` Thomas Streicher
2018-11-08 16:10 ` Thomas Streicher
2018-11-08 14:38 ` [HoTT] " Michael Shulman
2018-11-08 21:08 ` Thomas Streicher
2018-11-08 21:30 ` Michael Shulman
2018-11-09 11:56 ` Thomas Streicher [this message]
2018-11-09 13:46 ` Michael Shulman
2018-11-09 15:06 ` Thomas Streicher
2018-11-08 16:01 ` Thorsten Altenkirch
2018-11-08 19:39 ` Thorsten Altenkirch
2018-11-07 20:00 ` Michael Shulman
2018-11-08 21:35 ` Martín Hötzel Escardó
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