A Note on Coseparable Coalgebras

On Coseparable and Biseparable Corings

A relationship between coseparable corings and separable non-unital rings is established. In particular it is shown that an A-coring C has an associative A-balanced product. A Morita context is constructed for a coseparable coring with a grouplike element. Biseparable corings are defined, and a conjecture relating them to Frobenius corings is proposed.

A note on coalgebras and presheaves

We show that the category of coalgebras of a wide-pullback preserving endofunctor on a category of presheaves is itself a category of presheaves. This illustrates a connection between Jacobs’ temporal logic of coalgebras and Ghilardi and Meloni’s presheaf semantics for modal logic.

On descent for coalgebras and type transformations

We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

Topology on Coalgebras

On Coreflexive Coalgebras and Comodules over Commutative Rings

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called coreflexive coalgebras. Our approach in this note is an algebraically topological one. Introduction The concept of coreflexive coalgebras was studied, in the case of...