arXiv subjects

B. O. Bainson

Publications and source records attributed to B. O. Bainson.

2 recordsLinked to original sources

arXiv2017

The homology of principally directed ordered groupoids

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 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.

math.GR↗

arXiv2017

Cohomology and extensions of ordered groupoids

We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.

math.GR↗