Intrinsic entropy for generalized quasimetric semilattices

We introduce the notion of intrinsic semilattice entropy eh in the category Lqm of generalized quasimetric semilattices and contractive homomorphisms. By using appropriate categories X and functors F : X → Lqm, we find specific known entropies ehX on X as intrinsic functorial entropies, that is, as ehX = eh ◦ F. These entropies are the intrinsic algebraic entropy, the algebraic and the topological entropies for locally linearly compact vector spaces, the topological entropy for totally disconnected locally compact groups and the algebraic entropy for compactly covered locally compact abelian groups.