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An introduction to loopoids. (English) Zbl 1413.20037
Summary: We discuss a concept of loopoid as a non-associative generalization of Brandt groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as a framework for Lagrangian discrete mechanics.

MSC:
20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms)
20N05 Loops, quasigroups
22A22 Topological groupoids (including differentiable and Lie groupoids)
20N02 Sets with a single binary operation (groupoids)
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