  We introduce the notion of intrinsic semilattice entropy $\widetilde h$ in
the category $\mathcal L_{qm}$ of generalized quasimetric semilattices and
contractive homomorphisms. By using appropriate categories $\mathfrak X$ and
functors $F:\mathfrak X\to\mathcal L_{qm}$ we find specific known entropies
$\widetilde h_\mathfrak X$ on $\mathfrak X$ as intrinsic functorial entropies,
that is, as $\widetilde h_\mathfrak X=\widetilde h\circ F$. These entropies are
the intrinsic algebraic entropy, the algebraic and the topological entropies
for locally linearly compact vector spaces, the topological entropy for locally
compact totally disconnected groups and the algebraic entropy for locally
compact compactly covered abelian groups.
