Guilherme, Ricardo P.2025-02-122025-02-122024-06-170037-1912PURE: 109857687PURE UUID: b4ee9560-9f8b-4857-8089-ce59f3acd2dbScopus: 85196078750http://hdl.handle.net/10362/178927Funding Information: Open access funding provided by FCT|FCCN (b-on). This work is funded by national funds through the FCT– Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/ 10.54499/UIDP/00297/2020) (Center for Mathematics and Applications). Publisher Copyright: © The Author(s) 2024.The plactic monoids can be obtained from the tensor product of crystals. Similarly, the hypoplactic monoids can be obtained from the quasi-tensor product of quasi-crystals. In this paper, we present a unified approach to these constructions by expressing them in the context of quasi-crystals. We provide a sufficient condition to obtain a quasi-crystal monoid for the quasi-tensor product from a quasi-crystal monoid for the tensor product. We also establish a sufficient condition for a hypoplactic monoid to be a quotient of the plactic monoid associated to the same seminormal quasi-crystal.25413169engEquidivisibleHypoplactic monoidPlactic monoidQuasi-crystalAlgebra and Number Theoryjournal article10.1007/s00233-024-10436-8https://www.scopus.com/pages/publications/85196078750