Related papers: Notes on commutation of limits and colimits
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
The importance of accessible categories has been widely recognized; they can be described as those freely generated in some precise sense by a small set of objects and, because of that, satisfy many good properties. More specifically…
In these notes we briefly consider various situations related to infinite commutative semigroups, connected to convolutions and Fourier transforms.
Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that…
An example due to Pisier shows that two commuting, completely polynomially bounded Hilbert space operators may not be simultaneously similar to contractions. Thus, while each operator is individually similar to a contraction, the pair is…
Recently, different works proposed a new way to mine patterns in databases with pathological size. For example, experiments in genome biology usually provide databases with thousands of attributes (genes) but only tens of objects…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…
We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide…
We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second order and the…
In this paper we introduce filtration pairs for isolated invariant sets of continuous maps. We prove the existence of filtration pairs and show that, up to shift equivalence, the induced map on the corresponding pointed space is an…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…
We show that on an infinite set, there exist no other precomplete clones closed under conjugation except those which contain all permutations. Since on base sets of some infinite cardinalities, in particular on countably infinite ones, the…
The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…
The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…
Analogical proportions are 4-ary relations that read "A is to B as C is to D". Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference. This inference mechanism was…
We develop a Galois theory of commutative rings under actions of finite inverse semigroups. We present equivalences for the definition of Galois extension as well as a Galois correspondence theorem. We also show how the theory behaves in…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
Type A N-fold supercharge admits a one-parameter family of factorizations into product of N first-order linear differential operators due to an underlying GL(2,C) symmetry. As a consequence, a type A N-fold supersymmetric system can have…
Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is…
We contribute to the theory of (homotopy) colimits inside homotopy type theory. The heart of our work characterizes the connection between (graph-indexed) colimits in a type universe and colimits in coslices of the universe, called coslice…