A person who claims to be superior in culture and intellect to others is often referred to as an "Highbrow."

• Highbrow: This term is used to describe someone who considers themselves intellectually or culturally superior and has a refined taste in arts and intellectual pursuits.
• Aristocrat: This refers to someone from the upper class or nobility, but it doesn’t specifically imply a claim to cultural or intellectual superiority.
• Elite: This term denotes a group considered to be the best in a particular society or category, often including intellectual or cultural excellence, but it doesn’t specifically describe a person’s claim to superiority.
• Intellectual: This term refers to someone who is highly educated or knowledgeable, but it doesn’t necessarily imply they claim superiority over others.

So, Highbrow is the most fitting term for someone claiming to be superior in culture and intellect.