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?
 A: There is a preprint by Mike Shulman, Constructing Symmetric Monoidal Bicategories, which seems to treat the problem of constructing a symmetric monoidal bicategory from a symmetric monoidal double category. You can find it on arXiv, here: http://arxiv.org/abs/1004.0993
A: Kenny Courser has written a nice thesis on symmetric monoidal double categories and their applications:

*

*Kenny Courser, Open Systems: A Double Categorical Perspective, Ph.D. thesis, U. C. Riverside, 2020. Available at arXiv:2008.02394.

Also, Mike Shulman's paper mentioned above has a new installment, which explains symmetric monoidal double categories, the maps between them, and the maps between those - and how to turn these into symmetric monoidal double categories, and maps between them, and maps between those:

*

*L. W. Hansen and M. Shulman, Constructing symmetric monoidal bicategories functorially. Available at arXiv:1901.09240.

A: Symmetric Monoidal and Cartesian Double Categories as a Semantic Framework for Tile Logic by Roberto Bruni, José Meseguer, Ugo Montanari 
Mathematical Structures in Computer Science / Volume 12 / Issue 01 / February 2002, pp 53-90    DOI: http://dx.doi.org/10.1017/S0960129501003462, Published online: 26 February 2002
