Related papers: Model structures on finite total orders

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…

We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the…

We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…

We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models. We intro- duce a notion of rank of finitely generated models and we prove, when T has at most countably many…

In recent work, comonads and associated structures have been used to analyse a range of important notions in finite model theory, descriptive complexity and combinatorics. We extend this analysis to Hybrid logic, a widely-studied extension…

The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…

We provide a complete classification of the possible cofinal structures of the families of precompact (totally bounded) sets in general metric spaces, and compact sets in general complete metric spaces. Using this classification, we…

We define model structures on exact categories which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly…

For any finite totally ordered set, the multisets of intervals form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some…

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…

We study the signalling structure of higher order quantum maps from an order-theoretic perspective, building on the combinatorial characterization of higher order types by Bisio and Perinotti. We have shown in a previous work…

Examples of exact categories in representation theory are given by the category of Delta-filtered modules over quasi-hereditary algebras, but also by various categories related to matrix problems, such as poset representations or…

In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

Using the theory of extensions of L-infinity algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the Chevalley-Eilenberg and Harrison…

The Tamari lattice, defined on Catalan objects such as binary trees and Dyck paths, is a well-studied poset in combinatorics. It is thus natural to try to extend it to other families of lattice paths. In this article, we fathom such a…

We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…

We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded…