The homology of principally directed ordered groupoids

Bernard Oduoku Bainson; N. D. Gilbert

doi:10.4310/HHA.2020.v22.n2.a10

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 language	English
Pages (from-to)	163 – 172
Number of pages	10
Journal	Homology, Homotopy and Applications
Volume	22
Issue number	2
Early online date	15 Apr 2020
DOIs	https://doi.org/10.4310/HHA.2020.v22.n2.a10
Publication status	Published - 2020

Keywords

Colimit
Groupoid
Homology

ASJC Scopus subject areas

Mathematics (miscellaneous)

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KW - Groupoid

KW - Homology

UR - https://www.scopus.com/pages/publications/85086334982

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ER -

The homology of principally directed ordered groupoids

Abstract

Keywords

ASJC Scopus subject areas

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