Mag, wat kan? Over genetische manipulatie*

Left Kan Extensions Over !-Cat

An existing procedure to compute left Kan extensions over the ground category Set also computes left Kan extensions over the ground categories Cat, 2-Cat, n-Cat for any n and indeed !-Cat. Therefore extension data struc-tured in this manner already can make use of the left Kan extension notion of a best possible approximation. Examples include systems of labeled transition systems and certain h...

Categories Enriched over a Quantaloid: Isbell Adjunctions and Kan Adjunctions

Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory. It is proved that these two processes are functorial with infomorphisms playing as morphi...

Biuletyn Wat

In the paper we present some methods of constructing cryptosystems utilising chaotic dynamical systems that has been extensively developed last years. We start with a brief review of algorithms based on both the theory of continuous and discrete systems. Then we show our approach where the essence of chaos (that is the sensitivity of the trajectories of discrete chaotic dynamical systems to the...

Genetische Programmierung und Schach

Kan Extensions of Institutions

Institutions were introduced by Goguen and Burstall 8, 9, 10, 11] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphi...