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 define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category i...

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

We use the theory of institutions to capture the concept of a heterogeneous logical environment as a number of institutions linked by institution morphisms and comorphisms. We discuss heterogeneous specifications built in such environments, with inter-institutional specification morphisms based on both institution morphisms and comorphisms. We distinguish three kinds of heterogeneity: (1) speci...

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.

In this paper we investigate the structure of most general kind substitution shifts, including non-minimal ones and allowing erasing morphisms. We prove decidability all properties these morphisms with respect to shift space generated by iteration, such as aperiodicity, recognizability, irreducibility or minimality.