The paper first shows how the categorical theory of sequences is useful in explaining properties of the (word) differentiation of Brzozowski (1964). Then, the paper shows how a more general theory of languages, including both procedural and functional languages, should be constructed by using a switch proposition that extends the common equivalence between the general tensor and general hom functors of categories. Lastly, the paper offers a new way of approaching projectivity concepts of general relative homological algebra. The most interesting result is that there is a class of functors so that “functor-projectives” intersect projectives and injectives trivially, and behave correctly. Moreover, any non-zero abelian group is not Q⊗-projective.