Abstract Given a marked $$\infty $$ ∞ -category $$\mathcal {D}^{\dagger }$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">D† (i.e. an equipped with specified collection of morphisms) and functor $$F: \mathcal {D}\rightarrow ...

The category of all monads over many-sorted sets (and over other " set-like " categories) is proved to have coequalizers and strong coin-tersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms and have arbitrarily large joint pre-fixpoints. In contrast, coequalizers fail to exist e.g. for monads over the (presheaf) category of graphs. For more ge...

This case study applies techniques of formal program development by specification refinement and composition to the problem of concurrent garbage collection. The specification formalism is mainly based on declarative programming paradigms, the imperative aspect is dealt with by using monads. We also sketch the use of temporal logic in connection with monadic specifications.

For a small category K enriched over a suitable monoidal category V , the free completion of K under colimits is the presheaf category [K ,V ]. If K is large, its free completion under colimits is the V -category PK of small presheaves on K , where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed struct...

noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...