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.
ASJC Scopus subject areas
- Mathematics (miscellaneous)