Final answer:
The fornix is associated with the limbic system but is not considered a core structural component like the cingulate gyrus, amygdaloid body, and hypothalamus.
Step-by-step explanation:
The limbic system is a network of structures within the brain that are crucial for regulating emotions, fear, motivation, as well as playing a significant role in memory formation. When considering which structure is not a part of the limbic system among the options provided, the correct choice is the fornix. The fornix is indeed associated with the limbic system as a fiber tract, but when specifically referencing core structural components of the limbic system, the cingulate gyrus, amygdaloid body (amygdala), and hypothalamus are more directly considered parts of the limbic system as described in figures and text from various sources. It is important to clarify the differences between core components and associated structures when dealing with the limbic system. The cingulate gyrus helps regulate emotions and pain, the hypothalamus helps regulate homeostatic processes and interfaces with the endocrine system, and the amygdala is key in the processing of fear and emotional responses.