Related papers: On factorizations of graphical maps
This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah,…
If $X$ is a 2-Segal set, then the edgewise subdivision of $X$ admits a factorization system coming from upper and lower d\'ecalage. Using the correspondence between 2-Segal sets and unary operadic categories satisfying the blow-up axiom,…
We introduce the concept of a prenormed model of a particular kind of finitary single-sorted first-order theories, interpreted over a category with finite products. These are referred to as prealgebraic theories, for the fact that their…
We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category $\mathcal{C}$ over a field, the category of left $\mathcal{C}$--modules…
We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories with group actions and categories with graded hom spaces. We…
In this paper, we define a generalization of indexed categories and contextual categories which we call contextually indexed (contextual) categories. While contextual categories are models of ordinary type theories, contextually indexed…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
Given a smooth 3-fold $Y$, a line bundle $L \to Y$, and a section $s$ of $L$ such that the vanishing locus of $s$ is a normal crossings surface $X$ with graph-like singular locus, we present a way to reconstruct the singularity category of…
A moment category is endowed with a distinguished set of split idempotents, called moments, which can be transported along morphisms. Equivalently, a moment category is a category with an active/inert factorisation system fulfilling two…
An \'etale structure over a topological space $X$ is a continuous family of structures (in some first-order language) indexed over $X$. We give an exposition of this fundamental concept from sheaf theory and its relevance to countable model…
A generalization of an inverse system in a category was recently introduced, as well as that of the corresponding pro-category These so called the delay-inverse systems and delay-pro-category could potentially yield a new theory of (delay-)…
We construct so called Hall monoidal categories (and Hall modules thereover) and exhibit them as a categorification of classical Hall and Hecke algebras (and certain modules thereover). The input of the (functorial!) construction are…
We use the terms "$\infty$-categories" and "$\infty$-functors" to mean the objects and morphisms in an "$\infty$-cosmos." Quasi-categories, Segal categories, complete Segal spaces, naturally marked simplicial sets, iterated complete Segal…
We introduce and develop a structure theory of a new class of noncommutative rings - Galois orders, that generalize classical orders in noncommutative rings. Galois orders realized as certain subrings of invariants in skew semigroup rings.…
Motivated by the analogies between the projective and the almost quaternionic geometries, we study the generalized planar curves and mappings. We follow, recover, and extend the classical approach as developed by Mikes and Sinyukov. Then we…
We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erd\H{o}s. We also mention some related problems.
We compute the homotopy derivations of the properads governing even and odd Lie bialgebras as well as involutive Lie bialgebras. The answer may be expressed in terms of the Kontsevich graph complexes. In particular, this shows that the…
In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis.…
Refined algebraic domains are regions in the plane surrounded by finitely many non-singular real algebraic curves which may intersect with normal crossing. We are interested in shapes of such regions with surrounding real algebraic curves.…
It is well-known that the Lie algebra of homotopy non-trivial degree zero derivations of the properad of strongly homotopy Lie bialgebras $\mathcal{H}olieb$ can be identified with the Grothendieck-Teichmuller Lie algebra $\mathfrak{grt}$.…