Allegories for Database Modeling
Allegories are categories modeled upon the category of sets and binary relations (where sets are objects and binary relations are morphisms composed using joins). In this paper we present a new conceptual data modeling formalism based on the language of allegories. We show that allegories provide more convenient framework for modeling data than more traditional categorical approaches in which arrows are interpreted as functional dependencies and in which many to many or partial relationships have to be represented as spans. Finally, we demonstrate that by using allegories different than the allegory of sets and binary relations, for example the allegory of sets and lattice valued relations, one can model replicated data or data stored in a valid time temporal database.
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