Editing Limit (category theory) (section)

===Examples===
* Every [[representable functor]] ''C'' → '''Set''' preserves limits (but not necessarily colimits).  In particular, for any object ''A'' of ''C'', this is true of the covariant [[Hom functor]] Hom(''A'',&ndash;) : ''C'' → '''Set'''.
* The [[forgetful functor]] ''U'' : '''Grp''' → '''Set''' creates (and preserves) all small limits and [[filtered colimit]]s; however, ''U'' does not preserve coproducts. This situation is typical of algebraic forgetful functors.
* The [[free functor]] ''F'' : '''Set''' → '''Grp''' (which assigns to every set ''S'' the [[free group]] over ''S'') is left adjoint to forgetful functor ''U'' and is, therefore, cocontinuous. This explains why the [[free product]] of two free groups ''G'' and ''H'' is the free group generated by the [[disjoint union]] of the generators of ''G'' and ''H''.
* The inclusion functor '''Ab''' → '''Grp''' creates limits but does not preserve coproducts (the coproduct of two abelian groups being the [[Direct sum of abelian groups|direct sum]]).
* The forgetful functor '''Top''' → '''Set''' lifts limits and colimits uniquely but creates neither.
* Let '''Met'''<sub>''c''</sub> be the category of [[metric space]]s with [[continuous function]]s for morphisms. The forgetful functor '''Met'''<sub>''c''</sub> → '''Set''' lifts finite limits but does not lift them uniquely.