Ostensibly these are two domains of discourse with the psychological level predicated on the physiological level. An idealist philosopher might argue that physiology is a product
of cognition as opposed to a substrate
of cognition but this has no functional value from a scientific point of view. On the other hand, physiological models based solely on mechanistic processes fail to capture some the essence of "human consciousness" like the concept of "free will". It follows that current physiological models may be a necessary
platform for cognition but not a sufficient
platform, thus the "duality" you propose is not an isomorphism.