Infinitésimaux et intuitionnisme
Information systems in categories of valued relations.
The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.
Initial Completions.
Initial Morphisms and Monomorphisms.
Initial normal covers in bi-Heyting toposes
The dual of the category of pointed objects of a topos is semi-abelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes, actions are representable provided the topos admits an essential Boolean covering. This contains the...
Injective models of -disconnected simplicial sets
We generalize the results by G.V. Triantafillou and B. Fine on -disconnected simplicial sets. An existence of an injective minimal model for a complete -algebra is presented, for any -category . We then make use of the -category associated with a -simplicial set to apply these results to the category of -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent -simplicial set by means of its injective minimal model.
Injectives in arrow categories
Injectivity in the quasi-topo of separated presheaves on a complete Heyting algebra
Injectivity of polyhedra
Injectivity versus exponentiability
Injektive Objekte in gewissen Kategorien der Verbände
Inner actions and Galois -objects in a symmetric closed category
Innere Translationen der kleinen Kategorien
Integral Domain Type Representations in Sheaves and Other Topoi.
Integrating observational and computational features in the specification of state-based, dynamical systems
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system...
Integrating Observational and Computational Features in the Specification of State-Based, Dynamical Systems
We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system states...
Internal categories in a left exact cosimplicial category.
Internal crossed modules.
Internal monotone-light factorization for categories via preorders.
Internal object actions
We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module.