Ordered groupoids and the holomorph of an inverse semigroup

N. D. Gilbert*, E. A. McDougall

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap operation on an inverse semigroup: for groups these two constructions coincide. We present detailed calculations for semilattices of groups and for the polycyclic monoids.

Original languageEnglish
Pages (from-to)648-662
Number of pages15
JournalSemigroup Forum
Issue number3
Early online date11 Dec 2014
Publication statusPublished - Dec 2015


  • Endomorphism
  • Holomorph
  • Inverse semigroup
  • Ordered groupoid

ASJC Scopus subject areas

  • Algebra and Number Theory


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