Notes on enriched categories with colimits of some class.
On a conjecture by J. H. Smith.
On a generalized small-object argument for the injective subcategory problem
On corings and comodules
It is shown that the categories of -coalgebras for a commutative unital ring and the category of -corings for some -algebra as well as their respective categories of comodules are locally presentable.
On sifted colimits and generalized varieties.
On the existence of group localizations under large-cardinal axioms.
Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...
On von Neumann varieties.
Pointwise inductive limits in accessible categories. (Limites inductives point par point dans les catégories accessibles.)
Semi-abelian monadic categories.
Solving algebraic equations using coalgebra
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable...
Solving Algebraic Equations Using Coalgebra
Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable ...