Discussion of Homotopy Type Theory and Univalent Foundations
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* [HoTT] TOWARDS A DIRECTED HOMOTOPY TYPE THEORY
@ 2018-08-03 16:13 Ali Caglayan
  2018-08-03 19:07 ` [HoTT] " Ali Caglayan
  0 siblings, 1 reply; 2+ messages in thread
From: Ali Caglayan @ 2018-08-03 16:13 UTC (permalink / raw)
  To: Homotopy Type Theory


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A preprint has appeared on the arXiv outlining a directed HoTT by Paige 
Randall North. 

Just from skimming so far it appears to be a standard Martin-Lof with a 
core, op and hom-type.

The core type gives the set of objects of a type (I suppose types are now 
categories of sorts). The op type gives the opposite category, then the hom 
type is the directed path type. 

As far as I can tell this type theory has semantics in Cat.

I would be interested on others thoughts on this.

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* [HoTT] Re: TOWARDS A DIRECTED HOMOTOPY TYPE THEORY
  2018-08-03 16:13 [HoTT] TOWARDS A DIRECTED HOMOTOPY TYPE THEORY Ali Caglayan
@ 2018-08-03 19:07 ` Ali Caglayan
  0 siblings, 0 replies; 2+ messages in thread
From: Ali Caglayan @ 2018-08-03 19:07 UTC (permalink / raw)
  To: Homotopy Type Theory


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Just realised I didn't include a link:

https://arxiv.org/pdf/1807.10566.pdf

On Friday, 3 August 2018 17:13:14 UTC+1, Ali Caglayan wrote:
>
> A preprint has appeared on the arXiv outlining a directed HoTT by Paige 
> Randall North. 
>
> Just from skimming so far it appears to be a standard Martin-Lof with a 
> core, op and hom-type.
>
> The core type gives the set of objects of a type (I suppose types are now 
> categories of sorts). The op type gives the opposite category, then the hom 
> type is the directed path type. 
>
> As far as I can tell this type theory has semantics in Cat.
>
> I would be interested on others thoughts on this.
>

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