We discuss the use of relation lifting in the theory of setbased coalgebra. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavorial equivalence. On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullbacks, such as the monot...

We deene the continuum up to order isomorphism (and hence homeomorphism) as the nal coalgebra of the functor X !, ordinal product with !. This makes an attractive analogy with the deenition of the ordinal ! itself as the initial algebra of the functor 1; X, prepend unity, with both deenitions made in the category of posets. The variants 1; (X !), X o !, and 1; (X o !) yield respectively Cantor ...

We investigate how finitary functors on Set can be extended or lifted to finitary functors on Preord and Poset and discuss applications to coalgebra.

Combining traces, coalgebra and lazy-filtering channel configurations for parallel composition, we give a fully-abstract denotational semantics for the π-calculus under weak early bisimilarity.

For any dg algebra $A$ we construct a closed model category structure on $A$-modules such that the corresponding homotopy is compactly generated by are finitely and free over (disregarding differential). We prove this Quillen equivalent to of comodules certain, possibly nonconilpotent coalgebra, so-called extended bar construction $A$. This generalises complements certain aspects Koszul duality...

We develop the theory of special biserial and string coalgebras and other concepts from the representation theory of quivers. These theoretical tools are then used to describe the finite dimensional comodules and Auslander-Reiten quiver for the coordinate Hopf algebra of quantum SL(2) at a root of unity. We also describe the stable Green ring. Let C = k ζ [SL(2)] denote the quantized coordinate...

With each coassociative coalgebra, we associate an oriented graph. The coproduct ∆, obeying the coassociativity equation (∆ ⊗ id)∆ = (id ⊗ ∆)∆ is then viewed as a physical propagator which can convey information. We notice that such a coproduct is non local. To recover locality we have to break the coassociativity of the coproduct and restore it, in some sense by introducing another coproduct ∆̃...