Adjungierte Dreiecke, Colimites und Kan-Erweiterungen.
Zum Satz von Freyd und Kelly.
Injectivity versus exponentiability
Cantors Diagonalprinzip für Kategorien.
Abschwächungen des Adjunktionsbegriffs.
Covollständigkeit vollständiger Kategorien.
Remarks on topologically algebraic functors
Extensions of factorization systems
Completions of categories and initial completions
Orthogonal and prereflective subcategories
Strong regular and dense generators
Order-enriched solid functors
Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating...
Totality of colimit closures
Adámek, Herrlich, and Reiterman showed that a cocomplete category is cocomplete if there exists a small (full) subcategory such that every -object is a colimit of -objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions...
Natural weak factorization systems
In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category is introduced, as a pair (comonad, monad) over . The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories.
Lifting tensorproducts along non-adjoint functors
Composites of effective descent maps
Descent equivalence
Multiplicative structures over sup-lattices
Totality of product completions
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category by asking the Yoneda embedding to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion of . We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product...
A categorical guide to separation, compactness and perfectness.
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