On 25/11/2011, at 3:06 AM, Sebastian Kerkhoff wrote:
I believe it is a well-known fact that a potential duality arises when a single object essentially lives in two different categories.
Dear Sebastian This topic has been discussed in this forum before (e.g. Oct 2010) and I recommend looking at the past emails. I don't think anyone mentioned the following paper which uses the idea of an A-object in B (which is equally a B-object in A) to provide examples as stated in the title. F. Foltz, G.M. Kelly and C. Lair, Algebraic categories with few monoidal biclosed structures or none, J. Pure and Applied Algebra 17 (1980) 171–177. The work of Lambek and Rattray, such as Lambek, J.; Rattray, B. A. A general Stone-Gelfand duality. Trans. Amer. Math. Soc. 248 (1979), no. 1, 1–35, should also be emphasized. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]