From: Andrew Swan <wakeli...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Cc: wakeli...@gmail.com, awo...@cmu.edu, Thierry...@cse.gu.se
Subject: Re: [HoTT] Semantics of higher inductive types
Date: Wed, 7 Jun 2017 23:35:24 -0700 (PDT) [thread overview]
Message-ID: <9c8e516a-a09b-4632-8cd1-ccf7a0211cfd@googlegroups.com> (raw)
In-Reply-To: <CAOvivQwJ_Dd=HCVmsYL2sPtHCv4USrwHTBzP6E50aX-iuruoFg@mail.gmail.com>
[-- Attachment #1.1: Type: text/plain, Size: 717 bytes --]
>
> Why is there no LOG in this?
It's a little messy to write out the actual details, but it is possible for
each map f : X -> Y to use the subobject classifier and dependent products
to construct a "universal lifting problem" for f, where universal means
that every other lifting problem against a pushout product of monomorphism
and i-endpoint inclusion factors uniquely as a pullback followed by the
universal lifting problem. Then, once a filler for the universal lifting
problem has been chosen, it can be used to construct a filler for all the
other lifting problems. (This can also be seen as an instance of a general
result that holds in any locally small fibration with finitely complete
base).
[-- Attachment #1.2: Type: text/html, Size: 906 bytes --]
next prev parent reply other threads:[~2017-06-08 6:35 UTC|newest]
Thread overview: 25+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-05-25 18:25 Michael Shulman
2017-05-26 0:17 ` [HoTT] " Emily Riehl
2017-06-01 14:23 ` Thierry Coquand
2017-06-01 14:43 ` Michael Shulman
2017-06-01 15:30 ` Steve Awodey
2017-06-01 15:38 ` Michael Shulman
2017-06-01 15:56 ` Steve Awodey
2017-06-01 16:08 ` Peter LeFanu Lumsdaine
2017-06-06 9:19 ` Andrew Swan
2017-06-06 10:03 ` Andrew Swan
2017-06-06 13:35 ` Michael Shulman
2017-06-06 16:22 ` Andrew Swan
2017-06-06 19:36 ` Michael Shulman
2017-06-06 20:59 ` Andrew Swan
2017-06-07 9:40 ` Peter LeFanu Lumsdaine
2017-06-07 9:57 ` Thierry Coquand
[not found] ` <ed7ad345-85e4-4536-86d7-a57fbe3313fe@googlegroups.com>
2017-06-07 23:06 ` Michael Shulman
2017-06-08 6:35 ` Andrew Swan [this message]
2018-09-14 11:15 ` Thierry Coquand
2018-09-14 14:16 ` Andrew Swan
2018-10-01 13:02 ` Thierry Coquand
2018-11-10 15:52 ` Anders Mörtberg
2018-11-10 18:21 ` Gabriel Scherer
2017-06-08 4:57 ` CARLOS MANUEL MANZUETA
2018-11-12 12:30 ` Ali Caglayan
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=9c8e516a-a09b-4632-8cd1-ccf7a0211cfd@googlegroups.com \
--to="wakeli..."@gmail.com \
--cc="HomotopyT..."@googlegroups.com \
--cc="Thierry..."@cse.gu.se \
--cc="awo..."@cmu.edu \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).