Related papers: Reedy categories and their generalizations

Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce…

The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…

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 prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure.

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

We define the Grothendieck-Witt category over a fixed ground ring. In order to study the structure of this category, we introduce the general theory of Gysin functors and their associated categories of correspondences. The latter…

This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…

The main result of this paper utilizes the representation graph of a group $G$, $R(V,G)$, and gives a general construction of a diagrammatic category $\mathbf{Dgrams}_{R(V,G)}$. The proof of the main theorem shows that, given explicit…

Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…

We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…

Convolution algebras on maps from structures such as monoids, groups or categories into semirings, rings or fields abound in mathematics and the sciences. Of special interest in computing are convolution algebras based on variants of Kleene…

We give describe several models for $(\infty,n)$-categories, with an emphasis on models given by diagrams of sets and simplicial sets. We look most closely at the cases when $n \leq 2$, then summarize methods of generalizing for all $n$.

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…