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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]