Extensions in the theory of lax algebras.
Free algebras in varieties
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.
Geometric and higher order logic in terms of abstract Stone duality.
Hopf-Galois extensions for monoidal Hom-Hopf algebras
Hopf-Galois extensions for monoidal Hom-Hopf algebras are investigated. As the main result, Schneider's affineness theorem in the case of monoidal Hom-Hopf algebras is shown in terms of total integrals and Hopf-Galois extensions. In addition, we obtain an affineness criterion for relative Hom-Hopf modules which is associated with faithfully flat Hopf-Galois extensions of monoidal Hom-Hopf algebras.
Internal object actions
We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.
Introduction to coalgebra.
Leçons commentées sur les monades
Liftings of Stone's monadicity to spaces and the duality between the calculi of inverse and direct images
Monad compositions. I: General constructions and recursive distributive laws.
Monadic epimorphisms and applications
Monads of effective descent type and comonadicity.
Morita equivalence of algebraic theories
Note on a submonadicity
On Extension of Functors onto the Kleisli Category of the Inclusion Hyperspace Monad
It is proved that there exists no extension of any non-trivial weakly normal functor of finite degree onto the Kleisli category of the inclusion hyperspace monad.
On extension of functors to the Kleisli category of some weakly normal monads
The problem of extension of normal functors to the Kleisli categories of the inclusion hyperspace monad and its submonads is considered. Some negative results are obtained.
On extensions of lax monads.
On limits and colimits in the Kleisli category
Paths in double categories.
Points of affine categories and additivity.
Proarrows II