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Re: Getting people together to talk about Category Theory and RDF or :P JSON-LD, JWT, ...

From: Henry Story <henry.story@bblfish.net>
Date: Wed, 3 Jun 2020 10:06:48 +0200
Cc: Wayne Chang <wyc@fastmail.fm>, Henry Story <hjs@bblfish.net>, Ryan Wisnesky <ryan@conexus.com>, Credentials Community Group <public-credentials@w3.org>
Message-Id: <09940A39-A426-45EC-8182-3F1E0382ECDA@bblfish.net>
To: Brent Shambaugh <brent.shambaugh@gmail.com>
Hi all,

For those who want to learn Category Theory (because they are starting to find
it appear in programming circles with Monads, Applicatives, …) then David Spivak 
and Ryan’s work is a great way to move from knowledge of data to knowledge of CT,
and for that to inform back on Data. Indeed reading about Functorial Databases, 
one gets the feeling that CT is a essentially a database of mathematical concepts.

The early papers listed here are particularly easy to get into
   https://www.categoricaldata.net/papers

What is very interesting is that it turns out that RDF is a structure
known in CT as a Grothentieck Construction. Grothendieck being on of
the most famous mathematicians of the 20th Century, this is very noteworthy.
( https://en.wikipedia.org/wiki/Grothendieck_construction )
So of course this raises an intriguing question: what were mathematicians 
doing with ”RDF” in the 1970ies? 

Note that functorial Databases as described by those papers are functors into
Set, the category of Sets and Functions. So that should make you pause a little, 
and wonder if that can be right for RDF, since RDF is relational. (functions
are relations that have only one value).

There is a way to get these constructions in Set, but for a more intuitive 
version it is better to move to the ”bicategories of relations”
https://arxiv.org/abs/1706.00526
That paper reworks the same concepts but on the category Rel, of relations,
rather than Set. Actually we move one level up to 2 categories, where we 
have arrows between arrows (which we know as rdfs:subPropertyOf ). 
And that is where inferencing takes place. That point by itself is 
very interesting.

Now what has this got to do with Credentials? 
Well, credentials require what we know as Quads, Contexts or DataSets. 
Since one has to sign a document, one needs both the data constituting
the signature, and the data that is signed. Those two are different,
since one may want to sign a graph that contains a fake signature (say
in a police investigation).

This is actually what I have been searching for. I am interested
to see how DataSets are modelled in CT, to see if that can enlighten 
us over in the SemWeb standards, perhaps giving us the tools to give
us semantics of DataSets. I have quite a lot of ideas on how this can
be done, but I am not quite there yet. One good hunch is that it arises
as Indexed Strong Monads (indexed on a speaker), as Adjunctions and 
modalities are closely related…  

Henry


> On 2 Jun 2020, at 22:46, Brent Shambaugh <brent.shambaugh@gmail.com> wrote:
> 
> Henry Story, I have been talking to Ryan Wisnesky and Wayne Chang separately. I know that both you and Ryan are interested in Category Theory for RDF.
> Wayne is becoming aware of Ryan's work with Algebraic Databases and has extensive experience in the BlockChain space. He has worked with the Decentralized Identity Foundation
> and will be an upcoming chair for the Credentials Community Group.
> 
> I do expect that this conversation will migrate in some form to the credentials community group. Probably as a topic on the call. I cc'ed the list. 
> 
> I am bringing you all together because I felt that I had insufficient experience to explain the depths of Category Theory applied to RDF to Wayne.*
> 
> It will probably be useful for many reasons:
> David Spivak: Categorical Databases (implemented by Ryan)
> https://www.youtube.com/watch?v=bk36__qkhrk 
> 
> Programming with Math (Exploring Type Theory) -- { Bartosz Milewski ... lives in Seattle, worked with David Spivak and Brendan Fong on a Category Theory Course at MIT }
> https://www.youtube.com/watch?v=8AGWTWVOJ74
> 
> I do know that Ryan will be having a online Meetup for Category Theory this evening (7-9 PDT / Los Angeles Time): https://www.meetup.com/Category-Theory/ . 
> 
> Henry Story: https://bblfish.net/ , https://web-cats.gitlab.io/ (doing a PhD with CT applied to RDF) 
> Wayne Chang: https://consensys.net/ , https://identity.foundation/ 
> Ryan Wisnesky: https://www.categoricaldata.net/ , https://www.wisnesky.net/
> 
> In general: https://www.w3.org/community/credentials/ , https://ssimeetup.org/
> 
> Please let me know if we can move things forward. I don't know how things will go down. Is there broad. Is there narrow interest? Who will talk? Where, when, why?
> 
> Thanks for your time.
> 
> -Brent
> 
> * In my opinion, CT is useful for mapping schemas. Math gives a provably correct way to do it. I made me think, oh wait, when I saw all of the GraphQL queries for IPFS for various blockchains (on the graph?). You're also adding more for VC wallets? hmm... 

Henry Story

https://co-operating.systems
WhatsApp, Signal, Tel: +33 6 38 32 69 84‬ 
Twitter: @bblfish
Received on Wednesday, 3 June 2020 08:07:08 UTC

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