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 
> <https://arxiv.org/abs/1802.06718>
> 2. W-Types with Reductions and the Small Object Argument 
> <https://arxiv.org/abs/1802.07588>
>
> Comments, questions, corrections, etc are welcome.
>
> Best,
> Andrew
>