What IS reproduction?

It occurs to me that the question of abiogenesis isn't really about the development of life from non-life. What abiogenesis needs to explain is how we get from "mere" chemicals to a self-replicator capable of surviving, multiplying and crucially evolving.Although I suspect the first such replicators would be nothing we would recognise as life, evolution can then bridge the gap between there and organisms such as cyanobacteria we do recognise as life.