We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by a single parameter, the recombination rate r in [0,1]. The case of r = 0 coincides with the standard replicator dynamics. The opposite case of r = 1 corresponds to a setup in which each new agent learns each new strategic dimension from a different mentor, and combines these dimensions into her adopted strategy. We fully characterise stationary states and stable states under these dynamics, and we show that they predict novel behaviour in various applications.