A categorical approach to integration.
A characterization of K-ary algebraic categories.
A characterization of locally -presentable categories
A construction of -filtered bicolimits of categories
A Continuity Criterion for Functors.
A duality between infinitary varieties and algebraic theories
A duality between -ary varieties and -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal , whenever -small products commute with -colimits in , then must be a -filtered category. We nevertheless introduce the concept of -sifted colimits so that morphisms between -ary varieties (defined to be -ary, regular right adjoints) are precisely the functors...
A duality relative to a limit doctrine.
A note on direct-product decompositions
A note on -embeddings
A note on subobjects defined by limit construction
A Note on the Structure of Injective Diagrams.
Abschwächungen des Adjunktionsbegriffs.
Abstract physical traces.
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.
Adjungierte Dreiecke, Colimites und Kan-Erweiterungen.
Almost abelian categories
An anabelian definition of abelian homology
An example concerning set-functors
Applications of the induced morphism theorem in regular categories