Can non-human animals combine abstract representations much like humans do with language? In particular, can they entertain a compositional representation such as 'not blue'? Across two experiments, we demonstrate that baboons (Papio papio) show a capacity for compositionality. Experiment 1 showed that baboons can entertain negative, compositional, representations: they can learn to associate a cue with iconically related referents (e.g., a blue patch referring to all blue objects), but also to the complement set associated with it (e.g., a blue patch referring to all non-blue objects). Strikingly, Experiment 2 showed that baboons not only learn to associate a cue with iconically related referents, but can learn to associate complex cues (composed of the same cue and an additional visual element) with the complement object set. Thus, they can learn an operation, instantiated by this additional visual element, that can be compositionally combined with previously learned cues. These results significantly reduce any claim that would make the manipulation and combination of abstract representations a solely human privilege.