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arXiv · 1704.03689

The homology of principally directed ordered groupoids

B. O. Bainson·N. D. Gilbert
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Abstract

We present some homological properties of a relation $\beta$ on ordered groupoids that generalises the minimum group congruence for inverse semigroups. When $\beta$ is a transitive relation on an ordered groupoid $G$, the quotient $G / \beta$ is again an ordered groupoid, and construct a pair of adjoint functors between the module categories of $G$ and of $G / \beta$. As a consequence, we show that the homology of $G$ is completely determined by that of $G / \beta$, generalising a result of Loganathan for inverse semigroups.

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B. O. Bainson, N. D. Gilbert. 2017-04-12. The homology of principally directed ordered groupoids. https://arxiv.org/abs/1704.03689

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