On Sep 22, 2008, at 9:14 AM, Antoinette Arsic wrote: (01)
> Pat,
>
> "Well you did ask," :-) I could say that studies show that singing
> to my plants (music, gardening and botany) helps them grow. On a
> more serious note I would like a good intro to category theory as
> you have defined it here pertaining to math: "Category theory is a
> branch of pure
> mathematics, a kind of ultimate abstraction of algebra, which focusses
> on systems ('categories') defined by mappings "
> (02)
My own bible is "categories for the working mathematician" by
Saunders MacLane, (Springer 1971, ISBN 0-387-90036-5) but admittedly
this is only a 'introduction' if you already have a math degree, and
its probably now way out of date. I havn't had any need to scan recent
texts, I'm afraid. (03)
Pat (04)
> THanks,
> Antoinette
>
> SGIS
> Antoinette Arsic
> Sr. Systems Engineer
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> ________________________________________
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>[ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> ] On Behalf Of Pat Hayes [phayes@xxxxxxx]
> Sent: Saturday, September 20, 2008 6:05 PM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Axiomatic ontology
>
> On Sep 20, 2008, at 8:47 AM, Rob Freeman wrote:
>
>> I would welcome comments on a possible relationship between gauge
>> theories in physics, Category Theory in maths, and semantics.
>>
>
> Well, you did ask. These three topics have absolutely nothing whatever
> to do with one another. Gauge theories focus on symmetries in physical
> theory: that is, ways in which theories are invariant under various
> mathematical transformations. Category theory is a branch of pure
> mathematics, a kind of ultimate abstraction of algebra, which focusses
> on systems ('categories') defined by mappings . Semantics is concerned
> with the relationship between representations and what it is that they
> represent. One might as well ask for comments on a possible
> relationship between botany, music and gardening.
>
> Let me ask in return, what was it that suggested to you that these
> three topics might have any relationship?
>
> Pat
>
>
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> (05)
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