Re: rdf and category theory

 

Thank you very much for the resources, Antoine. 

My sincere
apologies I cannot offer a counterpart neither additional relevant
resopurces, now. 

As Henry mentions they are enough good to bring us a
wide focus. 

BTW: There is a certain weakness -- metaphorically
speaking and personally referring to my experience -- in comprehending
Topology, not _Topoi_ , one of the most interesting fields of
Mathematics which set-theoretic definitions and constructions may be
useful to introduce and establish analogies for the semantic field (
i.e.: imagine Sets as Spaces, and Relations as Structures ) ; 

As Henry
notes, RDF hasrelations and CT comes to help 

I'll have a look and
thank you very much, again, for the resources. 

Sincerely 

On
2014-04-17 00:09, henry.story@bblfish.net wrote: 

> On 11 Apr 2014, at
16:32, Gregg Reynolds <dev@mobileink.com [6]> wrote: 
> 
>> On Fri, Apr
11, 2014 at 8:30 AM, Antoine Zimmermann <antoine.zimmermann@emse.fr [4]>
wrote:
>> 
>>> There're a lot of resources available online and for free
about category theory.
>>> 
>>> Some examples:
>>> - Jirí Adámek, Horst
Herrlich, George E. Strecker. Abstract and Concrete Categories: The Joy
of Cats (524 pages). http://katmat.math.uni-bremen.de/acc/acc.pdf
[1]
>>> - Maarten M. Fokkinga. A Gentle Introduction to Category Theory:
the calculational approach.
http://wwwhome.ewi.utwente.nl/~fokkinga/mmf92b.pdf [2] (80 pages).
>>> -
Jaap van Oosten. Basic Category Theory (88 pages).
http://www.staff.science.uu.nl/~ooste110/syllabi/catsmoeder.pdf [3]
>>

>> One of the best is Robert Goldblatt's Topoi : The Categorial
Analysis of Logic [5]. He pays special attention to linking CT concepts
to both classic math and ordinary intuition.
> 
> I looked through
Robert Goldblatt's Topoi quickly [1] and indeed it is the book that
covers the subject probably most relevant to the semantic web community,
since it aims to show how logic can be derived from Category Theory. In
this area I found reading through the first part of Ralf Krömer's "Tool
and Object: A History and Philosophy of Category Theory" to also be very
interesting, as it gives an overview of the foundational debate in
Mathematics started by CT. 
> It's so odd that RDF is entirely about
relations just as CT is ( except that RDF is one to many whereas CT
arrows are functions). So I really look forward to understanding how
these two domains fit together, and perhaps how they complement each
other. 
> Henry 
> [1] Having read through half of "Conceptual
Mathematics" by Willima Lawvere and done most of the exercises there, I
am starting to be able to read a lot of these books much more easily. 
>

>> -Gregg
> 
> Social Web Architect 
> http://bblfish.net/ [7]

--


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Links:
------
[1]
http://katmat.math.uni-bremen.de/acc/acc.pdf
[2]
http://wwwhome.ewi.utwente.nl/~fokkinga/mmf92b.pdf
[3]
http://www.staff.science.uu.nl/~ooste110/syllabi/catsmoeder.pdf
[4]
mailto:antoine.zimmermann@emse.fr
[5]
http://homepages.mcs.vuw.ac.nz/~rob/books.html
[6]
mailto:dev@mobileink.com
[7] http://bblfish.net/
[8]
mailto:delfin@delfiramirez.info
[9] http://delfiramirez.info/
[10]
http://delfiramirez.blogspot.com/