Generalized heaps, inverse semigroups and Morita equivalence

Details Generalized heaps, inverse semigroups and Morita equivalence Generalized heaps, inverse semigroups and Morita equivalence

2011-04-13

arxiv.org/abs/1104.2458v1

Mathematics

Category Theory

Scientific paper

Inverse semigroups are the abstract counterparts of pseudogroups of transformations. The abstract counterparts of atlases in differential geometry are what Wagner termed `generalized heaps'. These are sets equipped with a ternary operation satisfying certain axioms. We prove that there is a bijective correspondence between generalized heaps and the equivalence bimodules, defined by Steinberg. Such equivalence bimodules are used to define the Morita equivalence of inverse semigroups. This paper therefore shows that the Morita equivalence of inverse semigroups is determined by Wagner's generalized heaps.

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