Re: Fred

["Joyal, André" <joyal.andre@uqam.ca>]

Dear John,  and category theorists,

The fact that every category has an opposite introduces 
a symmetry in mathematics that would not be there otherwise. 
The category of sets is not self dual, but a disjoint union of sets 
is a coproduct, dual to a product.  

Thurston does not show esteem for logic.
Most mathematicians are taking logic for granted; they just use it 
as a part of their natural language. 
It is obvious that human understanding depends on the 
the laws of thought, on logic. 
In a sense, category theory is a branch of mathematical logic,
since it greatly improves mathematical thinking in general.
A category theorist might say (not too loudly) that mathematical logic
is a branch of category theory.

Best,
andré

________________________________________
From: John Baez [baez@math.ucr.edu]
Sent: Friday, September 08, 2017 9:15 PM
To: categories
Subject: categories: Re: Fred

Dear Categorists -

Vaughan wrote:

>> There is one other anecdote about UACT, nothing to do with Fred, that I
>> have always loved. In the course of MSRI director Bill Thurston'
>> opening remarks, he said words to the effect that the notion of the
>> opposite of a category made him nauseous. This was the only meeting I
>> have ever attended where fully half the attendees drew in enough breath
>> to drop the air pressure by an audible amount.

Since "nauseous" means "causing nausea", perhaps Thurston's remark
had just sickened the audience.

Emily wrote:

> I’ll confess that the idea of an opposite category appearing as the
> codomain of a functor also makes me somewhat nauseated (the
> domain of course is no problem).

Now here is someone well-attuned to these subtleties of English!

I've always been delighted by opposite categories.  Sometimes I think
we live in one.  For example: if you flip forward in a book you
eventually reach the back, but if you go back far enough you reach
the foreword... and in the ancient past everything was younger.

I always tell my students that since category theory reduces all of
mathematics
to the study of arrows, and the only mistake you can make with an arrow is
to get confused about which way it's pointing, they should expect to spend
many hours confused about exactly this.

Best,
jb



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