text: This generalizes to the definition of exponentiation in a category in which finite direct products exist: in such a category, the functor  is, if it exists, a right adjoint to the functor  A category is called a Cartesian closed category, if direct products exist, and the functor  has a right adjoint for every .
  Repeated exponentiation
  Just as exponentiation of natural numbers is motivated by repeated multiplication, it is possible to define an operation based on repeated exponentiation; this operation is sometimes called hyper-4 or tetration. Iterating tetration leads to another operation, and so on, a concept named hyperoperation. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster than multiplication, which is faster-growing than addition, tetration is faster-growing than exponentiation. Evaluated at , the functions addition, multiplication, exponentiation, and tetration yield 6, 9, 27, and  () respectively.
  Limits of powers
  Zero to the power of zero gives a number of examples of limits that are of the indeterminate form 00. The limits in these examples exist, but have different values, showing that the two-variable function  has no limit at the point . One may consider at what points this function does have a limit.
  More precisely, consider the function  defined on . Then  can be viewed as a subset of  (that is, the set of all pairs  with ,  belonging to the extended real number line , endowed with the product topology), which will contain the points at which the function  has a limit.