Category systems are remarkably consistent across societies. Stable partitions for concepts relating to flora, geometry, emotion, color, and kinship have been repeatedly discovered across diverse cultures. Canonical theories in cognitive science argue that this form of convergence across independent populations, referred to as ‘cross-cultural convergence’, is evidence of innate human categories that exist independently of social interaction. However, a number of studies have shown that even individuals from the same population can vary substantially in how they categorize novel and ambiguous phenomena. Contrary to findings on cross-cultural convergence, this individual variation in categorization processes suggests that independent populations should evolve highly divergent category systems (as is often predicted by theories of social constructivism). These puzzling findings raise new questions about the origins of cross-cultural convergence. In this dissertation, I develop a new mathematical approach to cultural processes of category formation, which shows that whether or not independent populations create similar category systems is a function of population size. Specifically, my model shows that small populations frequently diverge in their category systems, whereas in large populations, a subset of categories consistently reach critical mass and spread, leading to convergent cultural trajectories. I test and confirm this prediction in a large-scale online social network experiment where I study how small and large social networks construct original category systems for a continuum of novel and ambiguous stimuli. I conclude by discussing the implications of these results for networked crowdsourcing, which harnesses coordination in communication networks to enhance content management and generation across a wide range of domains, including content moderation over social media and scientific classification in citizen science.