The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with either undeformed or q-deformed coalgebra symmetry are given, and their Liouville superintegrability is discussed. Among them, (quasi-maximally) superintegrable...

The notion of Hochschild homology a dg algebra admits natural dualization, the coHochschild coalgebra, introduced in [23] as tool to study free loop spaces. In this article we prove “agreement” for homology, i.e., that coalgebra C is isomorphic category appropriately compact C-comodules, from which Morita invariance follows. Generalizing case, define topological (coTHH) spectra, suspension spec...

We combine ideas coming from several fields, including modal logic, coalgebra, and set theory. Modally saturated trees were introduced by K. Fine in 1975. We give a new purely combinatorial formulation of modally saturated trees, and we prove that they form the limit of the final ωopchain of the finite power-set functor Pf . From that, we derive an alternative proof of J. Worrell’s description ...