  In recent work, comonads and associated structures have been used to analyse
a range of important notions in finite model theory, descriptive complexity and
combinatorics. We extend this analysis to Hybrid logic, a widely-studied
extension of basic modal logic, which corresponds to the bounded fragment of
first-order logic. In addition to characterising the various resource-indexed
equivalences induced by Hybrid logic and the bounded fragment, and the
associated combinatorial decompositions of structures, we also give
model-theoretic characterisations of bounded formulas in terms of invariance
under generated substructures, in both the finite and infinite cases.
