Category Set - Definition

This is an exemplary page in which we define the category of sets and functions, called Set\mathbf{Set}.


The category of sets and functions Set\mathbf{Set} is constituted of:

  • Objects: all sets;
  • Morphisms: Given sets XX and YY, the set Hom Set(X,Y)\text{Hom}_{\mathbf{Set}}(X,Y) is the set of all functions from XX to YY;
  • Identity morphisms: Given a set XX, its identity morphism id X\text{id}_X is the identity function XXX\to X, id X(x)=x\text{id}_X(x)=x;
  • Composition operation: The composition operation is the usual composition of functions.