V članku dokažemo strukturni rezultat o pravih razširitvah dvostranskih omejitvenih polgrup preko parcialnih delovanj. S tem posplošimo ustrezne rezultate za monoide in za inverzne polgrupe, hkrati ...slednje nadgradimo. V članku uvedemo in preučimo nekaj razredov parcialnih delovanj dvostranjskih omnejitvenih polgrup, ki posplošujejo parcialna delovanja monoidov in inverznih polgrup. Pokažemo, da obstaja adjungiranost med kategorijo ▫${\mathcal{P}}(S)$▫, objekti katere so prave razširitve omejitvene polgrupe ▫$S$▫ in kategorijo ▫${\mathcal{A}}(S)$▫, objekti katere so parcialna delovanja omejitvene polgrupe ▫$S$▫, ki zadoščajo določenim pogojem, ki so bili uvedeni v delu O'Carrolla. V kategoriji ▫${\mathcal{A}}(S)$▫ določimo dve izomorfni podkategoriji. Ena podkategorija je zrcalna, druga kozrcalna, vsaka izmed teh kategorij pa je ekvivalentna kategoriji ▫${\mathcal{P}}(S)$▫.
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