Generalized quasi-metric semilattices Dikranjan, Dikran; Giordano Bruno, Anna; Künzi, Hans-Peter ...
Topology and its applications,
03/2022, Letnik:
309
Journal Article
Recenzirano
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.
Motivated by a problem posed in 10, we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLatt
O
of join semilattices with bottom element. In ...particular, we show that there are only finitely many closure operators of both categories, and provide a complete classification. We use this result to deduce the known fact that epimorphisms of SLatt and SLatt
O
are surjective. We complement the paper with two different proofs of this result using either generators or Isbell's zigzag theorem.
