Richard Garner <rhgg2 <at> hermes.cam.ac.uk>
2008-08-13 16:29:23 GMT
What you call a cocategory enriched over V can also be
described as a category enriched over V^op. These have been
studied by Paddy McCrudden in his thesis under the name
"coalgebroids" (= many-object coalgebras). The main results
are on a generalised notion of Tannakian duality; and on
transfer of extra structure across this duality. See
 Paddy McCrudden, Categories of Representations of Coalgebroids,
Advances in Mathematics Volume 154, Issue 2, Pages 299-332
 Paddy McCrudden, Balanced Coalgebroids
Theory and Applications of Categories, Vol. 7, pp 71-147.
--On 12 August 2008 20:45 Toby Bartels wrote:
> I've been thinking idly about a concept dual to categories
> in much the same way that co-algebras are dual to algebras,
> and I've decided that I'd like to more about it.
> To be precise, if V is a monoidal category,
> then a category enriched over V has maps [A,B] (x) [B,C] -> [A,C],
> while a cocategory enriched over V has maps [A,C] -> [A,B] (x) [B,C].
> (You can fill in the rest of the definition for yourself.)
> Searching Google, this concept appears to be known (under this name)