The variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \(\ell \)-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \(\ell \)-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \(\ell \)-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated \(\ell \)-groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

各种（尖的）剩余格包括与代数逻辑相关的绝大多数代数类别，例如\（\ ell \） -基团，Heyting代数，MV-代数或De Morgan单半体。在异常值中，一个计算正模数格和其他形式的量子代数。我们建议使用一个通用的框架-指向左残基\（\ ell \）- groupoids-可以容纳所有剩余结构和量子结构。我们研究了尖的左残基\（\ ell \）- groupoids的子变体的格，它们的理想，并发展了一个左核理论。最后，我们扩展了剩余\（\ ell \）的连接完成理论的某些部分-groupoids到左残差的情况，为正模格子的MacLaren定理提供了新的证明。