  This article is part of the program of studying large-scale geometric
properties of totally disconnected locally compact groups, TDLC-groups, by
analogy with the theory for discrete groups. We provide a characterization of
hyperbolic TDLC-groups, in terms of homological isoperimetric inequalities.
This characterization is used to prove the main result of the article: for
hyperbolic TDLC-groups with rational discrete cohomological dimension $\leq 2$,
hyperbolicity is inherited by compactly presented closed subgroups. As a
consequence, every compactly presented closed subgroup of the automorphism
group $\mathrm{Aut}(X)$ of a negatively curved locally finite $2$-dimensional
building $X$ is a hyperbolic TDLC-group, whenever $\mathrm{Aut}(X)$ acts with
finitely many orbits on $X$. Examples where this result applies include
hyperbolic Bourdon's buildings.
  We revisit the construction of small cancellation quotients of amalgamated
free products, and verify that it provides examples of hyperbolic TDLC-groups
of rational discrete cohomological dimension $2$ when applied to amalgamated
products of profinite groups over open subgroups.
  We raise the question of whether our main result can be extended to locally
compact hyperbolic groups if rational discrete cohomological dimension is
replaced by asymptotic dimension. We prove that this is the case for discrete
groups and sketch an argument for TDLC-groups.
