Full subcategory

Summary

A full subcategory of a category $\mathcal{C}$ is a subcategory that keeps every morphism of $\mathcal{C}$ between any two of its objects. So it is fixed by its class of objects alone. Its inclusion functor is fully faithful. Most categories of "special" objects, such as abelian groups among groups or Hausdorff spaces among topological spaces, are full subcategories.