A Categorical Characterization of Accessible Domain

Accessible categories: The foundations of categorical model theory,

[F-S] D. Fremlin and S. Shelah, Pointwise compact and stable sets of measurable functions, manuscript, 1990. [G-G-M-S] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and geometrical structures in Banach spaces, Mem. Amer. Math. Soc, no. 378, Providence, RI, 1987. [G1 ] G. Godefroy, Parties admissibles d'un espace de Banach. Applications, Ann. Sci. Ecole Norm. Sup 4, (1...

Bisimulations and Unfolding in P-Accessible Categorical Models

We propose a categorical framework for bisimulations and unfoldings that unifies the classical approach from Joyal and al. via open maps and unfoldings. This is based on a notion of categories accessible with respect to a subcategory of path shapes, i.e., for which one can define a nice notion of trees as glueings of paths. We show that transition systems and presheaf models are instances of ou...

On minimal realization of IF-languages: A categorical approach

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...

Domain Theory for Concurrency —New Categorical Foundations

A categorical characterization of relative entropy on standard Borel spaces

We give a categorical treatment, in the spirit of Baez and Fritz, of relative entropy for probability distributions defined on standard Borel spaces. We define a category called SbStat suitable for reasoning about statistical inference on standard Borel spaces. We define relative entropy as a functor into Lawvere’s category [0,∞] and we show convexity, lower semicontinuity and uniqueness.