From: Michael Shulman <shu...@sandiego.edu>
To: "HomotopyT...@googlegroups.com" <homotopyt...@googlegroups.com>
Subject: Categories with 2-families
Date: Mon, 5 Mar 2018 13:29:56 -0800 [thread overview]
Message-ID: <CAOvivQwEH927TWF2OMFpeg9YYSArDDGiQRmtfJGjj0qsJzSQDA@mail.gmail.com> (raw)
By a standard construction (described for example at
https://ncatlab.org/nlab/show/categorical+model+of+dependent+types),
categories with families are equivalent to categories with attributes,
i.e. to comprehension categories that are discrete fibrations.
However, it seems to me that the attributes-to-families construction
can be applied to a non-discrete comprehension category as well,
producing something that one might call a "category with 2-families"
(or maybe "pseudo-families"?): a category C together with a
representable morphism Tm -> Ty of pseudofunctors C^op -> Cat. Have
such things been defined or used anywhere before?
next reply other threads:[~2018-03-05 21:30 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-03-05 21:29 Michael Shulman [this message]
2018-03-07 17:09 ` [HoTT] " Thomas Streicher
2018-03-07 20:15 ` Peter LeFanu Lumsdaine
2018-03-07 20:30 ` Thomas Streicher
2018-03-07 20:39 ` Peter LeFanu Lumsdaine
2018-03-07 21:01 ` Thomas Streicher
2018-03-07 22:16 ` Peter LeFanu Lumsdaine
2018-03-08 10:11 ` Thomas Streicher
2018-03-07 21:20 ` Michael Shulman
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