What are the possible varieties of cognition-artifact relations, and which dimensions are relevant for exploring these varieties? This question is answered in two steps. First, three levels of functional and informational integration between human agent and cognitive artifact are distinguished. These levels are based on the degree of interactivity and direction of information flow, and range from monocausal and bicausal relations to continuous reciprocal causation. In these levels there is a hierarchy of integrative processes in which there is an increasing degree of hybridization. Therefore, from a functional and informational level of abstraction, it becomes increasingly difficult to distinguish between agent and artifact in this hierarchy. Second, a multidimensional matrix for exploring cognition-artifact relations is sketched. The dimensions in the matrix include reliability, durability, trust, procedural and representational transparency, individualization, bandwidth, speed of information flow, distribution of computation, and cognitive and artifactual transformation. Together, these dimensions constitute a multidimensional space in which particular cognition-artifact relations can be located. The higher a particular cognition-artifact relation scores on these dimensions, the more integration and hybridization occurs, and the more tightly coupled the overall system is. It is then better, for explanatory reasons, to see agent and artifact as one cognitive system with a distributed informational architecture.