Abstract: In an era marked by the increasingly widespread application of various generative artificial intelligence (AI) technologies, AI has become a common medium for human cognition. A symbiotic cognitive mode between humans and AI has emerged, making it increasingly important to evaluate the status of AI within human-AI hybrid cognitive systems. Drawing on extended cognition theory and analyzing the cognitive attribution and cognitive item eligibility of AI, this paper argues that as human cognition extends to AI agents, human beings’ authority over cognitive attribution is neither shared nor usurped by AI. Although AI functions as a component of the cognitive system, its status depends on the delegation of human agency and the conferral of cognitive item eligibility; AI itself lacks independent authority over agency and eligibility for cognitive items. Nevertheless, considering that the realization of human intentionality typically relies on technological tools, the concept of “mediated–constitutive intentionality” can offer an explanatory framework for the interactive structure between humans and AI.