Capturing the playing style of professional soccer coaches is a complex, and yet barely explored, task in sports analytics. Nowadays, the availability of digital data describing every relevant spatio-temporal aspect of soccer matches, allows for capturing and analyzing the playing style of players, teams, and coaches in an automatic way. In this paper, we present coach2vec, a workflow to capture the playing style of professional coaches using match event streams and artificial intelligence. Coach2vec extracts ball possessions from each match, clusters them based on their similarity, and reconstructs the typical ball possessions of coaches. Then, it uses an autoencoder, a type of artificial neural network, to obtain a concise representation (encoding) of the playing style of each coach. Our experiments, conducted on soccer-logs describing the last four seasons of the Italian first division, reveal interesting similarities between prominent coaches, paving the road to the simulation of playing styles and the quantitative comparison of professional coaches.