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We construct the semi-infinite tensor structure on the semiderived category of quasi-coherent torsion sheaves on an ind-scheme endowed with a flat affine morphism into an ind-Noetherian ind-scheme with a dualizing complex. The semitensor…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
In this article we study the construction of characteristic classes for principal $G$-bundles equipped with an additional structure called transitionally commutative structure (TC structure). These structures classify, up to homotopy,…
We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.
As the second part of the treatise 'A General Theory of Concept Lattice', this paper speaks of the tractability of the general concept lattice for both its lattice structure and logic content. The general concept lattice permits a feasible…
Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their…
This is the eighth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (Part VIII), we construct the braided…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its…
It is common practice in both theoretical computer science and theoretical physics to describe the (static) logic of a system by means of a complete lattice. When formalizing the dynamics of such a system, the updates of that system…
Based on the orthogonal Labastida-Mari{\~n}o-Ooguri-Vafa conjecture made by L. Chen & Q. Chen [5], we derive an infinite product formula for Chern-Simons partition functions, which generalizes the Liu-Peng's [19] recent results to the…
Our constructions provide a systematic way to study cohomology pre-algebraic structures via classical cohomology, simplifying computations and enabling the use of established techniques.
We show how the $\tau$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined.
In the previous paper, the structure of the cut locus was determined for a class of surfaces of revolution homeomorphic to a cylinder. In this paper, we prove the structure theorem of the cut locus for a wider class of surfaces of…
We give a long exact sequence for the homology of a graded atomic lattice equipped with a sheaf of modules, in terms of the deleted and restricted lattices. This is then used to compute the homology of the arrangement lattice of a…
Let X be a right-angled building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group…
We define a free uniformly complete vector lattice over a set of generators and give its concrete representation as a space of continuous positively homogeneous functions.
Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical…
In this paper, we introduce the notion of modular class of a Lie algebroid $A$ equipped with a Nambu structure satisfying some suitable hypothesis. We also introduce cohomology and homology theories for such Lie algebroids and prove that…
Let A and B be lattices with zero. The classical tensor product, $A\otimes B$, of A and B as join-semilattices with zero is a join-semilattice with zero; it is, in general, not a lattice. We define a very natural condition: $A \otimes…