Hi Sarah I think Koudenburg had studied this for Virtual double categories of two-sided 2-fibrations, where the promorphisms are split two-sided 2-fibrations. Perhaps you might find that useful? Regards Siya *Siyabonga Mthimkhulu* *Heidelberg Laureate Forum Alumni* *Ph.D Student, Double CategoriesAfrican Institute for Mathematical Sciences, 5 Melrose Road, Muizenberg 7945, Cape Town, South Africa.______________________________________________________________________________________________________________________* *"Ad Eundum Quo Nemo Ante Iit." — Star Trek* *______________________________________________________________________________________________________________________* On Sun, 27 Sep 2026 at 9:51 PM, Dukic, S.M. (Sarah) via Categories < categories-list@categories.org.au> wrote:
Dear all,
I am wondering about a double category of fibrations. In particular, whether the usual 2-category *Fib* (fibrations, cartesian functors, and natural transformations) extends to a double category, and if so what the notion of promorphisms and cells would be. I'm thinking that the promorphisms might be something like 2-sided fibrations (as described by e.g. Loregian and Riehl). Has anyone worked this out?
I am very much looking forward to your responses!
All the best,
Sarah _______________________________________________ Categories mailing list -- categories-list@categories.org.au To unsubscribe send an email to categories-list-leave@categories.org.au