From mboxrd@z Thu Jan 1 00:00:00 1970 Date: Mon, 26 Feb 2018 00:32:46 -0800 (PST) From: Andrew Swan To: Homotopy Type Theory Message-Id: Subject: Two Papers on Lifting Problems and the Small Object Argument MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_Part_11825_2125232006.1519633966264" ------=_Part_11825_2125232006.1519633966264 Content-Type: multipart/alternative; boundary="----=_Part_11826_360738901.1519633966264" ------=_Part_11826_360738901.1519633966264 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Dear all, I've recently posted a pair of papers on the arXiv that might be of interest to some people on this list. Both are on my work on lifting problems in fibrations and the small object argument. An interesting side effect was that a construction used can be seen as a kind of higher inductive type generalising W-types (this is the subject of the second paper). 1. Lifting Problems in Grothendieck Fibrations 2. W-Types with Reductions and the Small Object Argument Comments, questions, corrections, etc are welcome. Best, Andrew ------=_Part_11826_360738901.1519633966264 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
Dear all,

I've recently posted a pa= ir of papers on the arXiv that might be of interest to some people on this = list. Both are on my work on lifting problems in fibrations and the small o= bject argument. An interesting side effect was that a construction used can= be seen as a kind of higher inductive type generalising W-types (this is t= he subject of the second paper).


Comments, questions, corrections, etc are welcome.

Best,
Andrew
------=_Part_11826_360738901.1519633966264-- ------=_Part_11825_2125232006.1519633966264-- From mboxrd@z Thu Jan 1 00:00:00 1970 Date: Mon, 26 Feb 2018 20:32:51 -0800 (PST) From: Ryan Wisnesky To: Homotopy Type Theory Message-Id: <9c883324-a6a2-4609-b4cb-b891bc4c787e@googlegroups.com> In-Reply-To: References: Subject: Re: Two Papers on Lifting Problems and the Small Object Argument MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_Part_137_575826007.1519705971341" ------=_Part_137_575826007.1519705971341 Content-Type: multipart/alternative; boundary="----=_Part_138_1665868874.1519705971341" ------=_Part_138_1665868874.1519705971341 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit In the categorical data project (http://categoricaldata.net/aql.html) we've recently run into lifting problems as 'database integrity constraints' and the small object argument as an algorithm known as 'the chase'. I'd love the chance to connect this to type theory - can we speak offline? On Monday, February 26, 2018 at 3:32:46 AM UTC-5, Andrew Swan wrote: > > Dear all, > > I've recently posted a pair of papers on the arXiv that might be of > interest to some people on this list. Both are on my work on lifting > problems in fibrations and the small object argument. An interesting side > effect was that a construction used can be seen as a kind of higher > inductive type generalising W-types (this is the subject of the second > paper). > > 1. Lifting Problems in Grothendieck Fibrations > > 2. W-Types with Reductions and the Small Object Argument > > > Comments, questions, corrections, etc are welcome. > > Best, > Andrew > ------=_Part_138_1665868874.1519705971341 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: quoted-printable
In the categorical data project (http://categoricaldata.ne= t/aql.html) we've recently run into lifting problems as 'database i= ntegrity constraints' and the small object argument as an algorithm kno= wn as 'the chase'. =C2=A0I'd love the chance to connect this to= type theory - can we speak offline? =C2=A0

On Monday, February 26, = 2018 at 3:32:46 AM UTC-5, Andrew Swan wrote:
Dear all,

I've recent= ly posted a pair of papers on the arXiv that might be of interest to some p= eople on this list. Both are on my work on lifting problems in fibrations a= nd the small object argument. An interesting side effect was that a constru= ction used can be seen as a kind of higher inductive type generalising W-ty= pes (this is the subject of the second paper).

=

Comments, questions, corrections, etc = are welcome.

Best,
Andrew
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