On 05/09/2010, at 5:41 AM, Aleks Kissinger wrote:
In the (bi)category Prof of categories and profunctors, the dual of an object is the dual category. Profunctors most certainly came later than the notions of categorical dual and dual objects (or at least their concrete counterparts, dual spaces), so this might just be a happy coincidence.
Very well put! I might add that an extra point needed is that Prof is a monoidal bicategory where the tensor product is the cartesian product of categories (it is not the cartesian product in Prof). And yes, Prof is compact, autonomous, rigid, whichever word you prefer, and the dual in Prof of a category A is A^{op}. In reading the literature, note that other names for Prof are Dist, Bimod and Mod. ==Ross
On Sat, Sep 4, 2010 at 5:46 AM, David Leduc <david.leduc6@googlemail.com
wrote: Are the notions of dual category and dual object related? If not, are there any good reasons to use the word "dual" for both notions?
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]