Geodesic
The homology of principally directed ordered groupoids
Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 163-172.

Voir la notice de l'article provenant de la source International Press of Boston

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 we 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.
DOI : 10.4310/HHA.2020.v22.n2.a10
Classification : 18G60, 20J05, 20L05
Keywords: groupoid, homology, colimit 
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B.O. Bainson; N.D. Gilbert. The homology of principally directed ordered groupoids. Homology, homotopy, and applications, Tome 22 (2020) no. 2, pp. 163-172. doi : 10.4310/HHA.2020.v22.n2.a10. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2020.v22.n2.a10/

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