Representation

You may be referring to:

• Linear representation: The most common meaning of the term when used in the context of groups. It refers to an action of a group on a vector space over a field.
• Permutation representation: It is another term for a group action on a set.
• Representation over a category: This is a more general meaning that encompasses both linear and permutation representations. It is a homomorphism from a group to the automorphism group of an object in the category.