nLab
function set

Function sets

Definitions

Given sets AA and BB, the function set A BA^B is the set of all functions from BB to AA. In the foundations of mathematics, the existence of such a set may be taken to follow from the existence of power sets, from the axiom of subset collection, or as an axiom (the axiom of function sets) in its own right.

Generalisations

Thinking of Set as a locally small category, this is a special case of a hom-set. Thinking of Set\Set as a cartesian closed category, this is a special case of an exponential object, which is a special case of an internal hom.

Revised on September 26, 2012 00:49:21 by Urs Schreiber (82.169.65.155)