Related papers: The B\'enabou-Roubaud theorem via string diagrams

In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed…

Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train…

Courcelle's Theorem is an important result in graph theory, proving the existence of linear-time algorithms for many decision problems on graphs whose tree-width is bounded by a constant. The purpose of this text is twofold: to provide an…

We show that a trivial case of Janelidze's categorical Galois theorem can be used as a key step in the proof of Joyal and Tierney's result on the representation of Grothendieck toposes as localic groupoids. We also show that this trivial…

We provide a somewhat geometric proof of a rigidity theorem by M. Ledoux and C. Xia concerning complete manifolds with non-negative Ricci curvature supporting an Euclidean-type Sobolev inequality with (almost) best Sobolev constant. Using…

In this paper we show that counting Grothendieck's dessins d'enfants is universal in the sense that some other enumerative problems are either special cases or directly related to it. Such results provide concrete examples that support a…

In 1982, Yano proposed a conjecture predicting the $b$-exponents of an irreducible plane curve singularity which is generic in its equisingularity class. In this article we prove the conjecture for the case of two Puiseux pairs and…

A descent conjecture of Wittenberg [Wit24, Conjecture 3.7.4] predicts that if all the twists of a rationally connected torsor over a smooth base satisfy weak approximation with Brauer-Manin obstruction, then so does the base. We give an…

We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions so that there is a model structure for local algebras, so…

We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…

We introduce the notion of $\mathbb{E}_\infty$-descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are $\mathbb{E}_\infty$-descendable. As an application, we prove a variant of…

The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…

We present the first formal correctness proof of Edmonds' blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and properties that allow the algorithm to run in…

We propose a hypothesis that all gauge theories are equivalent to a certain non-standard string theory. Different gauge groups are accounted for by weights ascribed to the world sheets of different topologies. The hypothesis is checked in…

We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of…

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method…

We develop in a consistent manner the Ostrogradski-Hamilton framework for gonihedric string theory. The local action describing this model, being invariant under reparametrizations, depends on the modulus of the mean extrinsic curvature of…

This article studies descent theory in the setting of Berkovich spaces. We give sufficient conditions for a given fibered category over the category of k-affinoid algebras to be a stack for the Berkovich analogue of the faithfully-flat…

To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common…