Related papers: A General Theory of Pointlike Sets

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…

In "On the calculation of some differential Galois groups" (Invent. Math. 87 (1987), no. 1), Katz defines the notion of a special flat connection on the complex affine line minus the origin, and he shows that the functor which restricts a…

We determine the nature of the fixed point sets of groups of order p, acting on complexes of distinguished p-subgroups (those p-subgroups containing p-central elements in their centers). The case when G has parabolic characteristic p is…

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.

Let $\mathbf G$ be a connected reductive algebraic group over an algebraically closed field, and let $s\in\mathbf G$ be a semisimple element. We show that the centraliser of $s$ is the semi-direct product of its identity component by its…

Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer, and G_\infty its absolute Galois group. In this article, we define a class of…

We present a categorical formulation of the Hamiltonian renormalisation programme for quantum field theories, establishing a systematic bridge between functional and lattice renormalisation. To this end, we introduce two categories, $Seq$…

We prove that if $\pi$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $\pi$-groups. In particular, when $\pi$ is the empty set, we obtain Henckell's decidability of…

We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a functor from the category of centralizer-respecting…

Polynomial functors are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect…

We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators.…

We prove that if the group of fixed points of a generic automorphism of a simple group of finite Morley rank is pseudofinite, then this group is an extension of a (twisted) Chevalley group over a pseudofinite field. On the way to obtain…

We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors. Inspired by the classical theory of…

For a group $G$ of not prime power order, Oliver showed that the obstruction for a finite CW-complex $F$ to be the fixed point set of a contractible finite $G$-CW-complex is the Euler characteristic $\chi(F)$. He also has the similar…

Given any pointed CW complex (X,x), it is well known that the fondamental group of X pointed at x is naturally isomorphic to the automorphism group of the functor which associates to a locally constant sheaf on X its fibre at x. The purpose…

In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point subgroup of GL(V). Motivated in parallel by questions in…

The purpose of this paper is to constructively develop a Galois theory on irreducible shifts of finite type (SFTs) and to analyze the automorphism groups of SFTs using this framework. Let $X$ and $Y$ be irreducible SFTs. We demonstrate that…

A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring and let $\mathcal{F}$ be an algebraically closed field of characteristic $0$. We introduce the category $\overline{\mathcal{F}_{Rpp_k}}$ of…