Received We show that the category whose objects are famidclies of Markov processes on Polish spaces, with a given transition kernel, and whose morphisms are transition probability preserving, surjective continuous maps has semi-pullbacks, i.e. for any pair of morphisms fi : Si ! S (i = 1; 2), there exists an object V and morphisms i : V ! Si (i = 1; 2) such that f1 1 = f2 2. This property hold...

Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most impor...

In the standard Category of Graphs, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer to these graph morphisms as Strict Morphisms. We relax the condition on the graphs allowing any number of edges to be incident to any two vertices, as well as...

We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.

In this paper, we represent L-domains by means of formal concept analysis. Based on the attributive continuous contexts, propose notions LDF-contexts and $${\mathcal {F}}$$ -morphisms show that they provide concrete representations Scott-continuous functions between them, respectively. Moreover, category with $$\mathcal {F}$$ is proven to be equivalent as morphisms.

(Berkovich spaces over $${\mathbb {Z}}$$ : étale morphisms).— We develop properties of unramified, and smooth morphisms between Berkovich . prove that they satisfy analogous to those schemes we provide analytification criteria. Our results hold for any valued field, rings integers a number field discrete valuation rings. Those cases are treated by unified way.