Foncteurs sous-objets et relations continues
Free algebras and automata realizations in the language of categories
Free algebras, input processes and free monads
From where do figurative algebras come ?
Generalizing substitution
It is well known that, given an endofunctor on a category , the initial -algebras (if existing), i.e., the algebras of (wellfounded) -terms over different variable supplies , give rise to a monad with substitution as the extension operation (the free monad induced by the functor ). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness),...
Generalizing Substitution
It is well known that, given an endofunctor H on a category C , the initial (A+H-)-algebras (if existing), i.e. , the algebras of (wellfounded) H-terms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [12] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete...
Generators and relations for as a monoidal 2-category.
Homotopy-theoretic aspects of 2-monads.
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.
Idempotent Triples and Completion.
Induced Functors on Categories of Algebras.
Inner actions and Galois -objects in a symmetric closed category
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.
La sucesión de tres términos en categorías algebraicas.
Languages for triples, bicategories and braided monoidal categories
Lax operad actions and coherence for monoidal -categories, rings and modules.
Leçons commentées sur les monades
Liftings of Stone's monadicity to spaces and the duality between the calculi of inverse and direct images
Localizations of Maltsev varieties.
Loop cohomology