Additive relation categories or algebras: Mac Lane, Hutchinson axioms and bi-modularity Original Research Article

It has been shown that Mac Laneʹs additive categories (1961) are essentially equivalent to bi-allegories; part of Hutchinsonsʹ axiomatic (1986) is also equivalent to bi-allegories. Certain clarifying results on rectangles and reflexive in the allegories are shown to give the expected bijection between the coreflexive and reflexive in bi-allegories. New categories are used as targets of image functors. The results of image functors for bi-allegories can easily be deduced from those of image functors for normal allegories.