Categorization is our ability to flexibly assign sensory stimuli into discrete, behaviorally relevant groupings. Categorical decisions can be used to study decision making more generally by dissociating category identity of stimuli from the actions subjects use to signal their decisions. Here we discuss the evidence for such abstract categorical encoding in the primate brain and consider the relationship with other perceptual decision paradigms. Recent work on visual categorization has examined neuronal activity across a hierarchically organized network of cortical areas in monkeys trained to group visual stimuli into arbitrary categories. This has revealed a transformation of visual-feature encoding in early visual cortical areas into more flexible categorical representations in downstream parietal and prefrontal areas. These neuronal category representations are encoded as abstract internal cognitive states because they are not rigidly linked with either specific sensory stimuli or the actions that the monkeys use to signal their categorical choices.