Related papers: Characterizing model structures on finite posets
We describe a general construction of finiteness spaces which subsumes the interpretations of all positive connectors of linear logic. We then show how to apply this construction to prove the existence of least fixpoints for particular…
To every affine real arrangement of hyperplanes we associate a family of diagrams of spaces over the face poset of the arrangement. We show that any cover of the complement of the complexification of the arrangement is homotopy equivalent…
A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and…
Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…
We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that…
The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…
We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of…
A quasi-schemoid is a small category with a particular partition of the set of morphisms. We define a homotopy relation on the category of quasi-schemoids and study its fundamental properties. As a homotopy invariant, the homotopy set of…
The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed…
2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…
A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we…
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
We study the problem of existence and uniqueness of homotopy colimits in stable representation theory, where one typically does not have model category structures to guarantee that these homotopy colimits exist or have good properties. We…
We show that C if is a proper model category, then the pro-category pro-C has a strict model structure in which the weak equivalences are the levelwise weak equivalences. The strict model structure is the starting point for many homotopy…
We show that basic homotopical notions such as homotopy sets and groups, connected and truncated maps, cellular constructions and skeleta, etc., extend to the setting of $(\infty,\infty)$-categories, as well as to presentable categories…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
We introduce a new class of poset edge labelings for locally finite lattices which we call $SB$-labelings. We prove for finite lattices which admit an $SB$-labeling that each open interval has the homotopy type of a ball or of a sphere of…
In this paper, we construct incomplete versions of the equivariant stable category; i.e., equivariant stabilization of the category of $G$-spaces with respect to incomplete systems of transfers encoded by an $N_\infty$ operad $\mathcal{O}$.…