Stokes, Tim E.2011-11-082011-11-082011Stokes, T.E. (2011). Axioms for function semigroups with agreement quasi-order. Algebra Universalis, 66(1-2), 85-98.https://hdl.handle.net/10289/5859The agreement quasi-order on pairs of (partial) transformations on a set X is defined as follows: (f, g) ≼ (h, k) if whenever f, g are defined and agree, so do h, k. We axiomatize function semigroups and monoids equipped with this quasi-order, thereby providing a generalisation of first projection quasi-ordered ∩-semigroups of functions. As an application, axiomatizations are obtained for groups and inverse semigroups of injective functions equipped with the quasi-order of fix-set inclusion. All axiomatizations are finite.enfunction semigroupagreement quasi-orderfix-set quasi-orderJournal Article10.1007/s00012-011-0152-1