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Some partial results on the cancellation law for the tensor product of complete lattices. (English) Zbl 07501179

Summary: In this paper we study the cancellation law for the tensor product in the category \(\mathsf{Sup}\) of complete lattices and join-preserving maps. First, we investigate the tensor product of generalized power-set lattices. Based on which, we prove that the cancellation law for the tensor product has a close relation to that for the cartesian product of posets, and give a class of complete lattices which do not satisfy the cancellation law for the tensor product. Then, we also investigate the cancellation law for particular subclasses of complete lattices.

MSC:

06B23 Complete lattices, completions
08B25 Products, amalgamated products, and other kinds of limits and colimits
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