Re: Dual category and dual object

[Toby Bartels <toby+categories@ugcs.caltech.edu>]

Michael Barr wrote:

>Toby Bartels wrote:

>>David Leduc wrote:

>>>Are the notions of dual category and dual object related?

>>On the other hand, we can say "opposite category" instead of "dual category",
>>especially since we denote the dual category of C by C^{op}.

>So you would say that complete atomic boolean algebras is just Set^{op}?
>Well I wouldn't.  They are, of course, equivalent, but the same.

I would say both "The dual category of Set is Set^{op}."
and "CABA is a dual category of Set."
(and also "CABA is an opposite category of Set.").
Actually, I would probably do the grammar differently:
"CABA is a category dual [or "opposite"] to Set.".

Leduc's original question didn't have an article in it;
you seem to have interpreted is with "a" while I interpreted it with "the".
(We also interpreted "dual object" differently.)


--Toby


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