On the structure of categories of coalgebras

Relating coalgebraic notions of bisimulation

“…1.4] have observed. The counterexample of [27] is easily adapted to the settings of the presheaf categories for name passing, correcting oversights in [19,22,48].…”

Topological systems and Artin glueing

“…It is the purpose of the rest of this paper to show the necessary and sufficient conditions for TopSys(T ) to have an algebraic flavor. To be able to use the already obtained technique we will slightly change the setting recalling one concept already well-known in the literature [32]. …”

“…On the other hand, the theory emerging is rather convenient and therefore deserves the attention of the reader. One should also be aware of the study of the category Gl(U ) in [12,32], the case there, however, being restricted to topos-like properties of the category in question. Since we are interested in quite a different area, the cited results are not directly applicable in our setting, apart from those mentioned in the previous section.…”

“…The motivation lies mostly in computer science since coalgebras (which are the dual of algebras) turned out to be suitable as models for certain types of automata and, more generally, for (transition and dynamical) systems [30,57]. Moreover, in [32,Section 5] some relations between coalgebras and Artin glueing are considered, based on the fact [69] that Gl(U ) can be identified with the category of coalgebras (B × Y) G , where the functor G is defined by G(A, X) = (A, X × U (A)) (the existence of the latter products is required). The authors of the paper are mostly interested in topos-like properties of Gl(U ) and that is quite off the goal of the current manuscript.…”

“…In [12] the modified condition was proved to be necessary as well. Moreover, [32] considered relationships between categories of coalgebras and categories obtained by Artin glueing. In this paper, however, we dwell upon a different topic related to the above-mentioned embedding of topology into algebra.…”