Related papers: On posetal and complete partial applicative struct…
The aim of this article is to give an expository account of the equivalence between modest sets and partial equivalence relations. Our proof is entirely self-contained in that we do not assume any knowledge of categorical realizability. At…
Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…
Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is…
We investigate a category of quantum posets that generalizes the category of posets and monotone functions. Up to equivalence, its objects are hereditarily atomic von Neumann algebras equipped with quantum partial orders in Weaver's sense.…
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
A rigorous derivation is provided for canonical correlations and partial canonical correlations for certain Hilbert space indexed stochastic processes. The formulation relies on a key congruence mapping between the space spanned by a second…
In arXiv:1104.4441 it was shown that any 1-quasi-hereditary algebra affords a particular basis which is related to a given partial order on the set of simple modules. We show that the modules generated by these basis-elements are also…
We study underlying geometric structures for integral variational functionals, depending on submanifolds of a given manifold. Applications include (first order) variational functionals of Finsler and areal geometries with integrand the…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…
The partition problem is a well-known basic NP-complete problem. We mainly consider the optimization version of it in this paper. The problem has been investigated from various perspectives for a long time and can be solved efficiently in…
Effect algebras and pseudoeffect algebras were introduced by Foulis, Bennett, Dvurecenskij and Vetterlein as so-called quantum structures which serve as an algebraic axiomatization of the logic of quantum mechanics. A natural question…
We introduce a notion of ``hereditarily antisymmetric'' operator algebras and prove a structure theorem for them in finite dimensions. We also characterize those operator algebras in finite dimensions which can be made upper triangular and…
Earlier, Lunts and Rosenberg studied a notion of compatibility of endofunctors with localization functors, with an application to the study of differential operators on noncommutative rings and schemes. Another compatibility -- of Ore…
It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…
We investigate predicative aspects of constructive univalent foundations. By predicative and constructive, we respectively mean that we do not assume Voevodsky's propositional resizing axioms or excluded middle. Our work complements…
D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. We give an equivalent condition for that this poset is a…