Bokstein homomorphism as a universal object

The universal covering homomorphism in o-minimal expansions of groups

Suppose that G is a definably connected, definable group in an ominimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism p̃ : G̃ −→ G is a locally definable covering homomorphism and π1(G) is isomorphic to the o-minimal fundamental group π(G) of G defined using locally definable covering homomorphisms. ∗With partial support from the FCT (Fundação para a Ci...

RDF Entailment as a Graph Homomorphism

Semantic consequence (entailment) in RDF is ususally computed using Pat Hayes Interpolation Lemma. In this paper, we reformulate this mechanism as a graph homomorphism known as projection in the conceptual graphs community. Though most of the paper is devoted to a detailed proof of this result, we discuss the immediate benefits of this reformulation: it is now easy to translate results from dif...

On characteristics of homomorphism and embedding universal graphs

We relate the existence problem of universal objects to the properties of corresponding enriched categories (lifts and expansions). Particularly, extending earlier results, we prove that for every countable set F of finite structures there exists a (countably) universal structure U for the class Forbh(F) (of all countable structures omitting a homomorphism from all members of F). In fact U is t...

Homomorphism and Embedding Universal Structures for Restricted Classes

This paper unifies problems and results related to (embedding) universal and homomorphism universal structures. On the one side we give a new combinatorial proof of the existence of universal objects for homomorphism defined classes of structures (thus reproving a result of [6]) and on the other side this leads to the new proof of the existence of dual objects (established by [32]). Our explici...

Universal Object Format