article published yes Dikran Dikranjan author Anna Giordano Bruno author Hans Peter Künzi author Nicolò Zava author c8b3499c-7a77-11eb-b046-aa368cbbf2ad0000-0001-8686-1888 Daniele Toller author HeEd department Motivated by the recent introduction of the intrinsic semilattice entropy, we study generalized quasi-metric semilattices and their categories. We investigate the relationship between these objects and generalized semivaluations, extending Nakamura and Schellekens' approach. Finally, we use this correspondence to compare the intrinsic semilattice entropy and the semigroup entropy induced in particular situations, like sets, torsion abelian groups and vector spaces. Elsevier2022 eng 0166-8641 00079183880001210.1016/j.topol.2021.107916 309 D. Dikranjan, A. Giordano Bruno, H.P. Künzi, N. Zava, D. Toller, Topology and Its Applications 309 (2022). Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. 2022. Generalized quasi-metric semilattices. Topology and its Applications. 309, 107916. Dikranjan, Dikran, Anna Giordano Bruno, Hans Peter Künzi, Nicolò Zava, and Daniele Toller. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>. Elsevier, 2022. <a href="https://doi.org/10.1016/j.topol.2021.107916">https://doi.org/10.1016/j.topol.2021.107916</a>. D. Dikranjan, A. Giordano Bruno, H. P. Künzi, N. Zava, and D. Toller, “Generalized quasi-metric semilattices,” <i>Topology and its Applications</i>, vol. 309. Elsevier, 2022. Dikranjan, Dikran, et al. “Generalized Quasi-Metric Semilattices.” <i>Topology and Its Applications</i>, vol. 309, 107916, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.topol.2021.107916">10.1016/j.topol.2021.107916</a>. Dikranjan, D., Giordano Bruno, A., Künzi, H. P., Zava, N., &#38; Toller, D. (2022). Generalized quasi-metric semilattices. <i>Topology and Its Applications</i>. Elsevier. <a href="https://doi.org/10.1016/j.topol.2021.107916">https://doi.org/10.1016/j.topol.2021.107916</a> Dikranjan D, Giordano Bruno A, Künzi HP, Zava N, Toller D. Generalized quasi-metric semilattices. <i>Topology and its Applications</i>. 2022;309. doi:<a href="https://doi.org/10.1016/j.topol.2021.107916">10.1016/j.topol.2021.107916</a> 104132021-12-05T23:01:44Z2024-10-09T21:01:16Z