Re: diagrams in computer algebra

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

I paste and copy some old posting to this list that I have kept. It
seems to me that they are relevant for your discussion.

e.d.

> I'd like to announce a selection of Web-based category theory
> demonstrations that I've put up at
> http://www.j-paine.org/cgi-bin/webcats/webcats.php . The page contains a
> number of buttons such as "generate and demonstrate an equaliser" and
> "generate and demonstrate a limit": clicking on one will generate
> an example of the construct in the category of finite sets, and display it
> as a listing of its objects and arrows, and as a diagram. For limits and
> colimits, the demos generate a small random graph, convert it to a
> diagram, then compute and display its limit or colimit.
>
> Comments would be very welcome. The demos are a bit of an experiment: I
> had some categorical algorithms lying around from other work, and thought
> it would be interesting to connect them to the Web.


> "If you could commission a computer demonstration of any categorical idea,
> what would you ask for? Could such demonstrations have helped you, or your
> students, learn tricky ideas? And, would you be willing to share the
> visualisations and metaphors that you have devised to explain these ideas
> to yourself or others?"
>
> We've started a thread on this topic at the n-Category Cafe',
> http://golem.ph.utexas.edu/category/2009/04/graphical_category_theory_demo.html
> . Anybody interested in using computers to demonstrate concepts from
> category theory, do please have a look there. I've just added an
> explanation of the techniques available for delivering demonstrations over
> the Web, and I mention one - the 3D modelling environment called Alice -
> that I think will eventually be brilliant for animating category theory,
> and many other topics besides.


> This is to tell, or remind, readers about the Web-based interactive
> category-theory demonstrations I have on my site. Perhaps of interest to
> new students now an academic year is starting. They're at
> http://www.j-paine.org/cgi-bin/webcats/webcats.php . After some preamble,
> this page contains a form divided into sections. Each section generates a
> particular construct in the category of finite sets: e.g. a colimit,
> equaliser, or initial object. You can input sets and arrows, or let the
> demo choose its own. The output includes a diagram, and text explaining
> it.
>
> Cheers,
>
> Jocelyn Paine
> http://www.j-paine.org
> +44 (0)7768 534 091
>
> Jocelyn's Cartoons:
> http://www.j-paine.org/blog/jocelyns_cartoons/



On 03/10/11 15:02, Michael J Healy wrote:
> Sergei,
>
> My colleagues and I have been looking for something like this for a project.  We need to be able to specify small categories as the completions of finite graphs we are given, extend these by specifying commutative diagrams, pullbacks, etc, of interest, then define functors generated from graph homomorphisms, and take colimits of diagrams in Cat, etc etc.  We haven't found anything that does all this.  So, we're programming it in Haskell---one of our grad students knows the language.   We'll be happy to share our experience and will probably make the code available.  It's a work in progress.
>
> Best regards,
> Mike Healy
>

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