Related papers: Explicit Morphisms in the Galois-Tukey Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the…

The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms have received a lot of attention in the literature. However, a…

Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.

It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…

We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.

Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…

Given a rational function of degree at least two defined over a number field k, we study the cardinality of the set of rational iterated preimages. We prove bounds for the cardinality of this set as the rational function varies in certain…

We prove several results in the theory of fusion categories using the product (norm) and sum (trace) of Galois conjugates of formal codegrees. First, we prove that finitely-many fusion categories exist up to equivalence whose global…

We investigate the canonicity of inequalities of the intuitionistic mu-calculus. The notion of canonicity in the presence of fixed point operators is not entirely straightforward. In the algebraic setting of canonical extensions we examine…

Based on the well-known cardinal characteristics $\mathfrak{s}$, $\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection…

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the…

Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…

In 1955 George Mackey suggested that there is a fundamental dichotomy in the unitary representation theory of locally compact second countable groups. He felt that there cannnot be a reasonable classification theory for the unitary…

We characterize continuum as the smallest cardinality of a family of compact sets needed to cover a locally compact group for which the Open Mapping Theorem does not hold.

The Jacobian conjecture over a field of characteristic zero is considered directly in view of the nonlinear partial differential equations it is associated with. Exploring the integrals of such partial differential equations, this work…

In Remarks on Galois Cohomology and Definability [2], Pillay introduced definable Galois cohomology, a model-theoretic generalization of Galois cohomology. Let $M$ be an atomic and strongly $\omega$-homogeneous structure over a set of…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…