Monads in double categories

Barr, 1983 Bénabou, 1967, Introduction to bicategories, vol. 47, 1 Burroni, 1971, T-catégories (catégories dans une triple), Cahiers de Topologie et Géometrie Diffeŕentielle Catégoriques, 12, 215 Ehresmann, 1963, Catégories structurées, Annales Scientifiques de l’École Normale Supérieure. Troisième Séries, 80, 349, 10.24033/asens.1125 Fiore, 2007, Pseudo algebras and pseudo double categories, Journal of Homotopy and Related Structures, 2, 119 Fiore, 2008, Model structures on the category of small double categories, Algebraic & Geometric Topology, 8, 1855, 10.2140/agt.2008.8.1855 Gambino, 2004, Wellfounded trees and dependent polynomial functors, vol. 3085, 210 N. Gambino, J. Kock, Polynomial functors and polynomial monads, 2010. ArXiv:0906.4931v2. Gordon, 1995, Coherence for tricategories, Memoirs of the American Mathematical Society, 117, 10.1090/memo/0558 Grandis, 1999, Limits in double categories, Cahiers de Topologie et Géometrie Diffeŕentielle Catégoriques, 40, 162 Grandis, 2004, Adjoint for double categories. Addenda to limits in double categories, Cahiers de Topologie et Géometrie Diffeŕentielle Catégoriques, 45, 193 Jacobs, 1999 Kelly, 1980, A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on, Bulletin of the Australian Mathematical Society, 22, 1, 10.1017/S0004972700006353 Kelly, 1974, Review of the elements of 2-categories, vol. 420, 75 Lack, 2002, The formal theory of monads II, Journal of Pure and Applied Algebra, 175, 243, 10.1016/S0022-4049(02)00137-8 Lane, 1998 Leinster, 2004 Maietti, 2010, Joyal’s arithmetic universes as a list-arithmetic pretopos, Theory and Applications of Categories, 24, 39 Moerdijk, 2000, Wellfounded trees in categories, Annals of Pure and Applied Logic, 104, 189, 10.1016/S0168-0072(00)00012-9 Nordstrom, 1990 Shulman, 2008, Framed bicategories and monoidal fibrations, Theory and Applications of Categories, 20, 650 S. Staton, Name-passing process calculi: operational models and structural operational semantics. Ph.D. thesis, University of Cambridge. Available as Computer Laboratory Technical Report no. 688. 2007. Street, 1972, The formal theory of monads, Journal of Pure and Applied Algebra, 2, 149, 10.1016/0022-4049(72)90019-9 Street, 1980, Fibrations in bicategories, Cahiers de Topologie et Géometrie Diffeŕentielle Catégoriques, 21, 111