On Wed, Jun 22, 2011 at 2:59 PM, Arnaud Bailly <span dir="ltr">&lt;<a href="mailto:arnaud.oqube@gmail.com">arnaud.oqube@gmail.com</a>&gt;</span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Hello Greg and Alexander,<br>Thanks for your replies. Funnily, I happen to own the 3 books you mentionned :-) My interest in category theory is a long standing affair...<br><br>Note that owning a book, having read (most of) it and knowing a theory (or at least its principles and main concepts) is really quite a different thing from being able to apply it. Although I am certainly able to understand the Yoneda lemma, I am certainly unable to </blockquote>
<div><br></div><div>Well, you&#39;re way ahead of me.  I don&#39;t even &quot;get&quot; adjunctions, to tell you the truth.  By which I mean that I have no intuition about them; it&#39;s not so hard to understand the formal definition, but it&#39;s another thing altogether to grasp the deep significance.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">recognize the opportunity of using that knowledge to derive some new knowledge about something else. And being able to define a topoi is very different from being able to construct one or infer one out of a given category. This is an actual limitation of myself of course. <br>
</blockquote><div><br></div><div>Indeed.  But I&#39;ll bet your next paycheck that eventually CT will replace set theory as the basic mode of thinking about math, even at elementary levels.  It just awaits that brilliant writer who can connect the dots appropriately.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<br>Alexander&#39;s advice about using diagrams and simple notations is something I often try to do and something which most of the times end in writing a bunch of functions and data types in Haskell... What I am really looking for is a more systematic way of thinking about systems (or system fragments, or components) in a categorical way, perhaps starting with a bunch of arrows in some abstract category with objects as components and trying to infer new objects out of categorical consturctions which are made possible by the current diagrams (eg. what would be a pullback in such a category ? What would be its meaning ? Does the question itself have a meaning ?). <br>

<br>Maybe this is really foggy and on the verge to fall into &quot;abstract nonsense&quot;...<br><br></blockquote><div>Long live abstract nonsense!</div><div><br></div><div>Completely off topic:  a few months ago I had an idea about using category theory to provide rigorous semantics for the web (esp. rdf stuff etc.)  I&#39;ll probably never find time to work out the details, but it&#39;s a fun exercise in any case; if you want to mess around with applying CT to the real world maybe you can coem up with improvements.  See <a href="http://blog.mobileink.com/2011/03/resource-token-exchange.html">http://blog.mobileink.com/2011/03/resource-token-exchange.html</a>.  It&#39;s a bit of a mess, and some of it I would radically revise, but it might give you some ideas, if you&#39;re interested in the semantic web thingee.</div>
<div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">Best regards,<br><font color="#888888">arnaud<br>
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