Topological Space Objects in a Topos II: ...-Completeness and ...-Cocompleteness.
Topological Structures On Classes I
Topological structures on classes I.
Topological Structures On Classes II
Topological structures on classes II.
Topologically-algebraic structure functors full reflective or coreflective restrictions of semitopological functors
Torsion free types
Torsion Theories in Non-Additive Categories.
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...
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...
Towards a logic of semiotic systems
The rationalistic denotational approach to semantics is not adequate for capturing the structural dimension of meaning, which is immanent in semiotic systems. The demand for a structural approach to semantics is intensified by a turn in Artificial Intelligence, introduced by Connectionism and Information Retrieval. This paper presents such a structural approach to semantics founded on the phenomenological and autopoietic paradigms and proposes a formalization with the help of category theory.
Towards an -category of cobordisms.
Trames et sémantiques catégoriques des systèmes de trames
Trees, inverse systems, and valuated vector spaces
Troesch complexes and extensions of strict polynomial functors
We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for for big enough (and we give a conjecture for smaller values of ). We also study the “twisting spectral sequence” converging to the extension groups between the...
Two examples of reflections
Über einen Satz von Gabriel zur Charakterisierung regulärer Colimites.
Über einen Typ von injektiven Klassen.
Über einige Zerlegungen in einer Kategorie
Un moyen d’extension aux catégories internes dans des propriétés de la catégorie