The homology of principally directed ordered groupoids

Bernard Oduoku Bainson, N. D. Gilbert

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Abstract

We present some homological properties of a relation β on ordered groupoids that generalises the minimum group congruence for inverse semigroups. When β is a transitive relation on an ordered groupoid G, the quotient G/β is again an ordered groupoid, and we construct a pair of adjoint functors between the module categories of G and of G/β. As a consequence, we show that the homology of G is completely determined by that of G/β, generalising a result of Loganathan for inverse semigroups.
Original languageEnglish
Pages (from-to)163 – 172
Number of pages10
JournalHomology, Homotopy and Applications
Volume22
Issue number2
Early online date15 Apr 2020
DOIs
Publication statusPublished - 2020

Keywords

  • Colimit
  • Groupoid
  • Homology

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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