Related papers: Term rewriting on nestohedra

Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we…

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

The primary goal of this article is to set up a general theory of coherent cellular approximations of the diagonal for families of polytopes by developing the method introduced by N. Masuda, A. Tonks, H. Thomas and B. Vallette. We apply…

With a view on applications in computing, in particular concurrency theory and higher-dimensional rewriting, we develop notions of $n$-fold monoid and comonoid objects in $n$-fold monoidal categories and bicategories. We present a series of…

Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…

A classic theorem by Steinitz states that a graph G is realizable by a convex polyhedron if and only if G is 3-connected planar. Zonohedra are an important subclass of convex polyhedra having the property that the faces of a zonohedron are…

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…

Dendroidal sets offer a formalism for the study of $\infty$-operads akin to the formalism of $\infty$-categories by means of simplicial sets. We present here an account of the current state of the theory while placing it in the context of…

There are several real spherical models associated with a root arrangement, depending on the choice of a building set. The connected components of these models are manifolds with corners which can be glued together to obtain the…

We consider facet-Hamiltonian cycles of polytopes, defined as cycles in their skeleton such that every facet is visited exactly once. These cycles can be understood as optimal watchman routes that guard the facets of a polytope. We consider…

The category of coherent sheaves over a noetherian scheme is very important for studying the properties of a given scheme. For noetherian schemes it is a well-known fact that the topology can be fully recovered from the corresponding…

A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…

We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion…

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…

We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…

The two operations, deletion and contraction of an edge, on multigraphs directly lead to the Tutte polynomial which satisfies a universal problem. As observed by Brylawski in terms of order relations, these operations may be interpreted as…

Tate cohomology has been generalised by several authors using different constructions that have applications in group theory, ring theory and homotopical algebra. Therefore, there is a need for a uniform account that explains why their…

The usual coherence theorem of MacLane for categories with multiplication assumes that a certain pentagonal diagram commutes in order to conclude that associativity isomorphisms are well defined in a certain practical sense. The practical…

We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…