Related papers: Enhanced finite triangulated categories
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
We give sufficient conditions to find all subtypes isomorphic to a subtype in a finite generalized ordered type.
Monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the…
Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen…
We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…
In this article, we introduce the notion of pre-$(n+2)$-angulated categories as higher dimensional analogues of pre-triangulated categories defined by Beligiannis-Reiten. We first show that the idempotent completion of a…
We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition…
Let $R$ be a commutative ring with identity. A unit $u$ of $R$ is called exceptional if $1-u$ is also a unit. When $R$ is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then…
We construct a category equivalent to the category $\mathbf{Mon}$ of monoids and monoid homomorphisms, based on categories with strict factorization systems. This equivalence is then extended to the category $\mathbf{Mon_s}$ of unital…
Given a foliation $\mathcal{F}$ on $X$ and an embedding $X\subseteq Y$, is there a foliation on $Y$ extending $\mathcal{F}$? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently…
Permutation polynomials have been a subject of study for a long time and have applications in many areas of science and engineering. However, only a small number of specific classes of permutation polynomials are described in the literature…
This paper concerns the generation time that measures the number of cones necessary to obtain an object in a triangulated category from another object. This invariant is called level. We establish level inequalities for enhanced…
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent…
In this paper we translate the necessary and sufficient conditions of Tanaka's theorem on the finiteness of effective prolongations of a fundamental graded Lie algebras into computationally effective criteria, involving the rank of some…
We give the multiplicity of terminal singularities on threefolds by simple calculation. Then we obtain the best inequalities for the multiplicity and the index. By using this, we can improve the boundedness number of terminal weak Q-Fano…
We construct a symmetric monoidal category $LIE^{MC}$ whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "enhanced" infinity morphisms between shifted L-infinity…
Following Lawvere's description of metric spaces using enriched category theory, we introduce a change in the base of enrichment that allows description of some aspects of (relativistic) causal spaces. All such spaces are Cauchy complete,…
In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…
We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0)…
In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…