Purpose: This article aims to understand the controversies present from the insertion of a disruptive technology in a new business model, Uber, in the urban mobility market of Belo Horizonte-MG. Originality/value: The actor-network theory allows us to describe innovation as technical and social, as well as to identify the sociomaterialities that enact and multiple realities from controversies in dispute. The proposal is original in investigating how a disruptive innovation is built as a “fact”, accompanying its stabilization processes. Design/methodology/approach: The research was operationalized from the actor-network theory itself, using cartography to follow the actors in their controversies. The data came mainly from newspapers, postings on social networks and legal materials accessed through the internet (from December 2014 to July 2017). For the presentation of the results, the mandala of actors who dispute positions in controversies and the hierarchical tree of the controversies were used. Findings: The arrangement was marked by several controversies that deal with the legitimacy of the application, the labor relations established by the innovation and the quality of the services provided, each supported by different actors, positions and arguments. Four types of technology identified in this arrangement were identified: 1. user technology; 2. service provision; 3. economic issues; and 4. Uber driver. It is understood, therefore, that the technology has multiple dimensions and is enacted of different forms, and that this arrangement has not yet stabilized.