Related papers: Cores over Ramsey structures

Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$ (e.g., if the Generalized Continuum Hypothesis holds), we develop a proof system for classical infinitary logic that includes heterogeneous quantification (i.e., infinite…

We state the Ramsey property of classes of ordered structures with closures and given local properties. This generalises many old and new results: the Ne\v{s}et\v{r}il-R\"{o}dl Theorem, the author's Ramsey lift of bowtie-free graphs as well…

In 2012 M. Soki\'c proved that the class of all finite permutations has the Ramsey property. Using different strategies the same result was then reproved in 2013 by J. B\"ottcher and J. Foniok, in 2014 by M. Bodirsky and in 2015 yet another…

This article is concerned with classes of relational structures that are closed under taking substructures and isomorphism, that have the joint embedding property, and that furthermore have the Ramsey property, a strong combinatorial…

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal…

In contrast with the Hovey correspondence of abelian model structures from two compatible complete cotorsion pairs, Beligiannis and Reiten give a construction of model structures on abelian categories from one hereditary complete cotorsion…

We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.

We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…

For a category $\mathcal E$ with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simplicial objects in $\mathcal E$, generalising the Kan--Quillen…

We develop the homotopy theory of semisimplicial sets constructively and without reference to point-set topology to obtain a constructive model for $\omega$-groupoids. Most of the development is folklore, but for a few results the author is…

Motivated by algebraic structures appearing in Rational Conformal Field Theory we study a construction associating to an algebra in a monoidal category a commutative algebra ({\em full centre}) in the monoidal centre of the monoidal…

We show that the idempotent completion of an n-angulated category admits a unique n-angulated structure such that the inclusion is an n-angulated functor, which satisfies a universal property.

We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…

We present different ways of endowing a particular category of graphs with Quillen model structures. We show, among other things, that the core of a graph can be seen as its homotopy type in an appropriate Quillen model structure, and that…

A new, self-contained, proof of a coherence result for categories equipped with two symmetric monoidal structures bridged by a natural transformation is given. It is shown that this coherence result is sufficient for…

The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…

In this paper we show that a countable structure admitting a finite monomorphic decomposition has finite big Ramsey degrees if and only if so does every monomorphic part in its minimal monomorphic decomposition. The necessary prerequisite…

We construct of the main object of the Partite Lemma as the colimit over a certain diagram. This gives a purely category theoretic take on the Partite Lemma and establishes the canonicity of the object. Additionally, the categorical point…

In this article, we investigate homogeneous versions of certain nonlinear Ramsey-theoretic results, with three significant applications. As the first application, we prove that for every finite coloring of $\mathbb{Z}^+$, there exist an…

We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…