# symmetric monoidal double categories?

Let me preface this by saying that I don't know much category theory.

I am running into a situation where I have a double category and additionally there is a multiplication. Moreover, choosing either the vertical or the horizontal arrows makes my thing a symmetric monoidal category. Has this structure been studied somewhere?

• As far as I understand this (among other things) will be treated in Gaitsgory and Rozenblyum's upcoming book. – Adam Gal Apr 25 '14 at 13:21