In online or blended environments, the Community of Inquiry (CoI) framework sets that a meaningful educational experience derives from the interrelation of teaching, social and cognitive presences. Each presence is subdivided, resulting in a structure in ten categories at the basis for the CoI survey instrument. Although the survey structure in three presences was repeatedly validated in the literature, the categories within presences were not and were consequently investigated in this study. High internal consistencies between items of each category demonstrated that the structure is reliable. Its convergent and discriminant validity were confirmed using multi-group confirmatory factor analyses, that further allowed to reinforce the construct validation by evaluating its factorial invariance across independent samples collected in two universities and varying in gender and age (n1 = 343; n2 = 420). To assess its discriminant validity and because high estimated correlations between categories were observed, alternative structures in eight, seven and six factors were also compared to the original ten-category structure. They were all valid despite yielding inferior fits. The partial structural invariance of CoI structures in categories were also confirmed across groups. Next, a CoI structure in three presences resulted in an insufficient fit to data across independent groups. Much more conclusively, a second-order structure including both presences and categories demonstrated a very good fit to the data, highlighting the importance of categories to reflect students' perceptions. This paper, although presented at a conceptual level, enlightens the potential of studying the influence of categories on each other, learning outcomes, or to identify areas of improvement in online and blended courses by relying on meaningful and trustful categories that further characterize the well-known presences.