In this paper we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous crossover, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals similarities and differences between genetic systems based on these operations. It also reveals that the notion of schema emerges naturally from the model's equations even for the strangest of recombination operations. The study provides a variety of fixed points for the case where recombination is used alone, which generalise Geiringer's manifold.