Looking for results on preservation of 2-coproducts
Dear all, I'm interested in finding some results in the literature on bicategories with 2-coproducts. In particular, I'm interested in the symmetric 2-monoidal structure induced by 2-coproducts, the essentially unique symmetric pseudomonoid structure on each object with respect to this 2-monoidal structure, and preservation of all the above structures by left adjoint 2-functors. I think I could work through this myself if I had to, but I'd prefer to just cite someone else's work if I can. Perhaps this has been worked out in a thesis somewhere? Cheers, Jamie. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Hi ``Cartesian bicategories II'' by A. Carboni, G.M. Kelly, R.F.C. Walters, and R.J. Wood in TAC Vol. 19, 2008, No. 6, pp 93-124, gives the details showing that a bicategory with bicategorical finite products has a canonical symmetric monoidal structure. (This is used there to show that a cartesian bicategory also has a canonical symmetric monoidal structure.) Best regards, Richard
Dear all,
I'm interested in finding some results in the literature on bicategories with 2-coproducts. In particular, I'm interested in the symmetric 2-monoidal structure induced by 2-coproducts, the essentially unique symmetric pseudomonoid structure on each object with respect to this 2-monoidal structure, and preservation of all the above structures by left adjoint 2-functors.
I think I could work through this myself if I had to, but I'd prefer to just cite someone else's work if I can. Perhaps this has been worked out in a thesis somewhere?
Cheers, Jamie.
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On 15/12/2011, at 7:44 AM, Jamie Vicary wrote:
I'm interested in finding some results in the literature on bicategories with 2-coproducts.
Dear Jamie At the abstract level of bicategories, coproducts are the same as products. That structure is exactly what Max Kelly and colleagues were working on when Max died: 92. A. Carboni, G.M. Kelly, R.F.C. Walters, and R.J. Wood, Cartesian bicategories II, Theory and Applications of Categories 19 (2008) 93–124. Even in some applications, we do have coproducts and moreover cocompleteness in the hom categories. Then the coproducts are the products (2-dimensional direct sums). See 85. [also see 18] Cauchy characterization of enriched categories, Reprints in Theory and Applications of Categories 4 (2004) 1-16. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
-
Jamie Vicary -
rjwood＠mathstat.dal.ca -
Ross Street