Re: abstraction of notation from sets.

[Aleks Kissinger <aleks0@gmail.com>]

\epsilon is often used informally to mean an object or an arrow is contained
in a category C. I.e. a \in C is shorthand for a \in ob(C) or a \in ar(C),
when its interpretation is obvious from context.

Barr and Wells (Toposes, Triples and Theories, 1984) uses set inclusion
notation in an interesting way, thinking of arrows rather as "generalised
elements" of objections. So, they'll write something like f \in^A B instead
of f : A -> B, which should be read "f is an A-element of B". When the
category is sets and A = {*}, this is the usual notion of element. This
notion gives the right kind of intuition when working and categories that
are a lot like sets, especially toposes. The language also admits a
particularly beautiful way to express the Yoneda lemma.

"The (normal) elements of FA are the same as the hom(-,A)-elements of F."

a

On Wed, Feb 24, 2010 at 12:43 AM, <peasthope@shaw.ca> wrote:

> When S is a set, the notation "a \epsilon S" is familiar.
> Is this ever extended to CT?  All the texts I recall use
> natural language such as "A is an object of C".  What if
> a more symbolic notation is required?
>
> Thanks,       ... Peter E.
>
>

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