Related papers: Lifting independence along functors

Given commutative, unital rings $A$ and $B$ with a ring homomorphism $A\to B$ making $B$ free of finite rank as an $A$-module, we can ask for a "trace" or "norm" homomorphism taking algebraic data over $B$ to algebraic data over $A$. In…

In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to "unital, associative universal…

A classical approach to investigate a closed projective scheme $W$ consists of considering a general hyperplane section of $W$, which inherits many properties of $W$. The inverse problem that consists in finding a scheme $W$ starting from a…

Subobject independence as morphism co-possibility has recently been defined in [2] and studied in the context of algebraic quantum field theory. This notion of independence is handy when it comes to systems coming from physics, but when…

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

Let $R$ denote a 2-fir. The notions of F-independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F-independence in terms of dimension of…

Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a…

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…

With the aid of the concept of stable independence we can construct, in an efficient way, a compact representation of a semi-graphoid independence relation. We show that this representation provides a new necessary condition for the…

We provide a new description of the hom functor on weak $\omega$-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a…

We study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes. This is possible surprisingly often: we show that many of the standard examples of moduli stacks are determined by their…

The assignment (nonstable K_0-theory), that to a ring R associates the monoid V(R) of Murray-von Neumann equivalence classes of idempotent infinite matrices with only finitely nonzero entries over R, extends naturally to a functor. We prove…

A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted…

In this paper we construct an entire function of two variables having the property that its values and its partial derivatives of any order at any distinct algebraic points are algebraically independent. Such an entire function is generated…

An independent set in a simple graph $G$ is a set of pairwise non-adjacent vertices in $G$. The independence polynomial of $G$, denoted by $I_G$ is defined as $1 + a_1 z + a_2 z^2+\cdots+a_d z^{d}$, where $a_i$ denotes the number of…

For an adjoint pair $(F, G)$ of functors, we prove that $G$ is a separable functor if and only if the defined monad is separable and the associated comparison functor is an equivalence up to retracts. In this case, under an idempotent…

In this paper, we introduce the notion of conditionally bi-free independence in an amalgamated setting. We define operator-valued conditionally bi-multiplicative pairs of functions and construct operator-valued conditionally bi-free moment…

Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…