How individuals think about opposing or paradoxical categories influences their social relationships. We found that Chinese managers were more likely than US managers to categorize attempts to outperform others as an instance of both competition and cooperation. Further, the Chinese managers were more likely than the US managers to perceive a given working relationship as being both cooperative and competitive. The two findings were linked: culturally-guided beliefs about whether the cooperation-competition paradox should be integrated or kept separate influenced how individuals understood their social relationships. More broadly, the implication is that category membership and relations between categories are guided by cultural influences distinct from the particulars of the categories themselves that normally enter into cognitive science research on categories. In addition, those categorization choices are consequential for the network of social relationships individuals form.