"If you deprive cholesterol from the brain, then you directly affect the machinery that triggers the release of neurotransmitters," said Shin. "Neurotransmitters affect the data-processing and memory functions. In other words -- how smart you are and how well you remember things."

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More saturated fat, less dementia.

https://www.psychologytoday.com/blog/the-optimalist/201310/y...

"Two forms of fat that are vitally important for brain health are cholesterol and saturated fat. In the Mayo Clinic study mentioned above, it was found that those individuals consuming the most saturated fat experienced a 36% reduction in risk for developing dementia. And this comes on the heels of data now indicating that saturated fat consumption has absolutely no relevance in the area of cardiovascular risk as recently described by Dr. Glen Lawrence in the journal, Advances in Nutrition."

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This study seems to imply that large amounts of dietary cholesterol may not be needed for brain function though...

http://europepmc.org/abstract/med/1880610