The "Smart City" (SC) concept revolves around the idea of embodying cutting-edge ICT solutions in the very fabric of future cities, in order to offer new and better services to citizens while lowering the city management costs, both in monetary, social, and environmental terms. In this framework, communication technologies are perceived as subservient to the SC services, providing the means to collect and process the data needed to make the services function. In this paper, we propose a new vision in which technology and SC services are designed to take advantage of each other in a symbiotic manner. According to this new paradigm, which we call "SymbioCity", SC services can indeed be exploited to improve the performance of the same communication systems that provide them with data. Suggestive examples of this symbiotic ecosystem are discussed in the paper. The dissertation is then substantiated in a proof-of-concept case study, where we show how the traffic monitoring service provided by the London Smart City initiative can be used to predict the density of users in a certain zone and optimize the cellular service in that area. ; Comment: 14 pages, submitted for publication to MDPI Sensors Special Issue on Smart Cities