* [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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