We present a model that describes the structure in the responses of different brain areas to a set of stimuli in terms of "stimulus categories" (clusters of stimuli) and "functional units" (clusters of voxels). We assume that voxels within a unit respond similarly to all stimuli from the same category, and design a nonparametric hierarchical model to capture inter-subject variability among the units. The model explicitly captures the relationship between brain activations and fMRI time courses. A variational inference algorithm derived based on the model can learn categories, units, and a set of unit-category activation probabilities from data. When applied to data from an fMRI study of object recognition, the method finds meaningful and consistent clusterings of stimuli into categories and voxels into units.