Intrinsic entropy for generalized quasimetric semilattices

Abstract

We introduce the notion of intrinsic semilattice entropy [Formula: see text] in the category [Formula: see text] of generalized quasimetric semilattices and contractive homomorphisms. By using appropriate categories [Formula: see text] and functors [Formula: see text], we find specific known entropies [Formula: see text] on [Formula: see text] as intrinsic functorial entropies, that is, as [Formula: see text] 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.