Related papers: Homomorphisms and Structural Properties of Relatio…
Homomorphism duality pairs play crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be…
A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we…
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in terms of disjoint unions of dual…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We address the problem of characterizing $H$-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of…
We study dualities between classes of relational topological structures, given by Hom-functors. We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative noetherian ring. In particular, we extend the isomorphism properties of certain natural morphisms from homologically…
A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…
Homomorphisms between relational structures are not only fundamental mathematical objects, but are also of great importance in an applied computational context. Indeed, constraint satisfaction problems (CSPs), a wide class of algorithmic…
We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…
We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying…
We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to classify all binary relations with at most $6$ points in the…
In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
We deal with the complete-intersection property of maximally differential ideals. Also, we connect the Gorenstein homology of derivations to the Gorenstein property of the base rings. These equipped with some applications.
This article is devoted to investigations of a structure and homomorphisms of microbundles. Microbundles are generalizations of manifolds. For manifolds it was studied when their families of homomorphism can be supplied with the manifold…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…