Abstract:HCI researchers' and practitioners' awareness of intersectionality has been expanding, producing knowledge, recommendations, and prototypes for supporting intersectional populations. However, doing intersectional HCI work is uniquely expensive: it leads to a combinatorial explosion of empirical work (expense 1), and little of the work on one intersectional population can be leveraged to serve another (expense 2). In this paper, we explain how representations employed by certain analytical design methods correspond to type abstractions, and use that correspondence to identify a (de)compositional model in which a population's diverse identity properties can be joined and split. We formally prove the model's correctness, and show how it enables HCI designers to harness existing analytical HCI methods for use on new intersectional populations of interest. We illustrate through four design use-cases, how the model can reduce the amount of expense 1 and enable designers to leverage prior work to new intersectional populations, addressing expense 2.