We introduce a notion of an integral along bimonoid homomorphism as simultaneous generalization the and cointegral bimonoids. The purpose this paper is to characterize existence specific integral, called normalized generator in terms kernel cokernel homomorphism. volume on abelian category dimension vector spaces order groups. In applications, we show that there exists nontrivial partially defi...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

A relational structure is homomorphism-homogeneous if any homomorphism between its finite substructures extends to an endomorphism of the structure in question. In this note, we characterise all permutations on a finite set enjoying this property. To accomplish this, we switch from the more traditional view of a permutation as a set endowed with two linear orders to a different representation b...

Twisted Alexander invariant is defined for a finitely presentable group G and a representation of G and a surjective homomorphism of G to a free abelian group. In this talk, we introduce some examples and some properties of the twisted Alexander invariant. Moreover, as an application, we consider a partial order on the set of prime knots. Let K be a knot and G(K) the knot group. For two prime k...

We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG Gmeans that the knowledge represented by Q is deducible from the knowledge represented ...

We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

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Let Gn,k denote the Kneser graph whose vertices are the n-element subsets of a (2n + k)-element set and whose edges are the disjoint pairs. In this paper we prove that for any non-negative integer s there is no graph homomorphism from G4,2 to G4s+1,2s+1. This confirms a conjecture of Stahl in a special case.