Categories of partial maps

AbstractThis paper attempts to reconcile the various abstract notions of “category of partial maps” which appear in the literature. First a particular algebraic theory (p-categories) is introduced and a representation theorem proved. This gives the authors a coherent framework in which to place the various other definitions. Both algebraic theories and theories which make essential use of the poset-enriched structure of partial maps are discussed. Proofs of equivalence are given where possible and counterexamples where known. The paper concludes with brief sections on the representation of partial maps and on partial algebras