Structure Species and Constructive Functors

Abstract

This communication is in essence a note tying together the structure theory of Bourbaki and the categorical structure theory exemplified in the works of Sonner, and Hedrlin, Pultr, and Trnkova, to name a few. The work of Bourbaki [1] appeared in 1957, and quietly succumbed to the explosion of category theory. Sonner [6] used the nomenclature of Bourbaki to classify certain types of functors, while Hedrlin et al use the functor approach, studying structures by way of the associated forgetful functors. More discussion of this approach appears in section 3.