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- W4300606437 abstract "Cross-connection theory provides the construction of a semigroup from its ideal structure using small categories. A concordant semigroup is an idempotent-connected abundant semigroup whose idempotents generate a regular subsemigroup. We characterize the categories arising from the generalised Green relations in the concordant semigroup as consistent categories and describe their interrelationship using cross-connections. Conversely, given a pair of cross-connected consistent categories, we build a concordant semigroup. We use this correspondence to prove a category equivalence between the category of concordant semigroups and the category of cross-connected consistent categories. In the process, we illustrate how our construction is a generalisation of Nambooripad's cross-connection analysis of regular semigroups. We also identify the inductive cancellative category associated with a pair of cross-connected consistent categories." @default.
- W4300606437 created "2022-10-03" @default.
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- W4300606437 date "2018-06-28" @default.
- W4300606437 modified "2023-10-16" @default.
- W4300606437 title "Cross-connection structure of concordant semigroups" @default.
- W4300606437 doi "https://doi.org/10.48550/arxiv.1806.11031" @default.
- W4300606437 hasPublicationYear "2018" @default.
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