Associativity in monoids and categories
Atoms in the family of coreflective subcategories of uniform spaces
Axiomatic cohesion.
Axiomatic cohomology of operator algebras
Axiomatisation de la catégorie des catégories
Baer sums and fibered aspects of Mal'cev operations
Balanced category theory.
Bimorphisms in pro-homotopy and proper homotopy
A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. The category is balanced if every bimorphism is an isomorphism. In the paper properties of bimorphisms of several categories are discussed (pro-homotopy, shape, proper homotopy) and the question of those categories being balanced is raised. Our most interesting result is that a bimorphism f:X → Y of is an isomorphism if Y is movable. Recall that is the full subcategory of consisting of...
Boolean Galois theories.
Booleanization of uniform frames
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.
Bounded functors, finite limits and an application of injective topoi
Calcul des courants induits et des forces électromagnétiques dans un système de conducteurs mobiles
Calcul des satellites et présentations des bimodules à l'aide des carrés exacts
Calculating limits and colimits in pro-categories
We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. We also correct some mistakes in the literature on this topic.
Cantors Diagonalprinzip für Kategorien.
Carrés exacts et carrés déductifs
Cartesian bicategories. II.
Categoría exponencialmente fiel: Un teorema sobre functores adjuntos.
Let P be a small category and A(B) a category such that the functor A → AP (B → BP) determined by the projection functor A x P → A (B x P → B) has an adjoint for all small category P. A functor G: B → AP has an adjoint functor if and only if it has and adjoint functor "via" evaluation. If Q is another small category and F: P → Q an arbitrary functor, the functor AF: AQ → AP has an adjoint functor.
Categorial refinements and their relation to reflective subcategories
Categorical abstract data type (CADT)