2-categorical tools in the theory of concrete categories
A cartesian closed extension of a category of affine schemes
A categorical approach to integration.
A characterization of locally -presentable categories
A completion functor for Cauchy groups.
A duality relative to a limit doctrine.
A generalized duality theorem for structure functors
A note on free regular and exact completions and their infinitary generalizations.
A note on the exact completion of a regular category, and its infinitary generalizations.
A note on the generalized reflexion of Guitart and Lair
Absolute colimits in enriched categories
Abstract pro arrows I
Adhesive and quasiadhesive categories
We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Adhesive and quasiadhesive categories
We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Adjoints, multi-adjoints, pluri-adjoints.
Adjungierte Dreiecke, Colimites und Kan-Erweiterungen.
Applications of the induced morphism theorem in regular categories
Balanced category theory.
Boolean Galois theories.
Categorical domain theory: Scott topology, powercategories, coherent categories.