This text contains an introduction to the theory of limits over the category of presentations, with examples of different well-known functors like homology or derived functors of non-additive functors in the form of derived limits. The theory of so-called fr-codes is also developed. This is a method that shows how different functors from the category of groups to the category of abelian groups, such as group homology and tensor products of abelianization, can be coded as sentences in the alphabet with two symbols f and r.