The term co-creativity has been used to describe a wide variety of human-AI assemblages in which human and AI are both involved in a creative endeavor. In order to assist with disambiguating research efforts, we present an ontology of co-creative systems, focusing on how responsibilities are divided between human and AI system and the information exchanged between them. We extend Lubart’s original ontology of creativity support tools with three new categories emphasizing artificial intelligence: computer-as-subcontractor, computer-as-critic, and computer-as-teammate, some of which have sub-categorizations.