Abstract
The category \(\mathbb {DRDL}{'}\), whose objects are c-differential residuated distributive lattices satisfying the condition \(\textbf{CK}\), is the image of the category \(\mathbb {RDL}\), whose objects are residuated distributive lattices, under the categorical equivalence \(\textbf{K}\) that is constructed in Castiglioni et al. (Stud Log 90:93–124, 2008). In this paper, we introduce weak monadic residuated lattices and study some of their subvarieties. In particular, we use the functor \(\textbf{K}\) to relate the category \(\mathbb {WMRDL}\), whose objects are weak monadic residuated distributive lattices, and the category \(\mathbb {WMDRDL}{'}\), whose objects are pairs formed by an object of \(\mathbb {DRDL}{'}\) and a center weak universal quantifier.
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Acknowledgements
The authors are extremely grateful to the editor and the referee for their valuable comments and helpful suggestions which help to improve the presentation of this paper. This work is supported by the National Natural Science Foundation of China (12001423, 61976244,12171294, 12001413,11871320), Major Program of the National Social Science Foundation of China (20 &ZD047), Natural Science Foundation of Shaanxi Province (2020JQ-762, 2021JQ-580, 2021JQ-579).
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Wang, J.T., She, Y.H., He, P.F. et al. On Categorical Equivalence of Weak Monadic Residuated Distributive Lattices and Weak Monadic c-Differential Residuated Distributive Lattices. Stud Logica 111, 361–390 (2023). https://doi.org/10.1007/s11225-022-10026-1
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DOI: https://doi.org/10.1007/s11225-022-10026-1