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Related papers: Characterizing model structures on finite posets

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This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is…

Combinatorics · Mathematics 2026-03-05 Jing-Wen Gao , Xiao-Song Yang

We enlarge the category of bornological coarse spaces by adding transfer morphisms and introduce the notion of an equivariant coarse homology theory with transfers. We then show that equivariant coarse algebraic $K$-homology and equivariant…

K-Theory and Homology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…

Category Theory · Mathematics 2019-08-20 Hoang Kim Nguyen

We characterize $A_\infty$-structures that are transfers over a chain homotopy equivalence or a quasi-isomorphism, answering a question posed by D. Sullivan. Along the way, we present an obstruction theory for weak $A_\infty$-morphisms over…

Algebraic Topology · Mathematics 2021-06-18 Martin Markl , Christopher L. Rogers

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…

Algebraic Topology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting…

Optimization and Control · Mathematics 2017-01-23 Alain Rapaport , Alejandro Rojas-Palma , Jean-Raynald De Dreuzy , Hector Ramirez

In this article, we construct a cofibrantly generated model structure on the category of spaces stratified over a fixed poset, and show that it is Quillen-equivalent to a category of diagrams of simplicial sets. Then, considering all those…

Algebraic Topology · Mathematics 2021-03-10 Sylvain Douteau

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

Rings and Algebras · Mathematics 2020-05-05 Ilya Zhdanovskiy

A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…

Fluid Dynamics · Physics 2023-08-08 Jian-Jun Shu

We construct model category structures on various types of (marked) *-categories. These structures are used to present the infinity categories of (marked) *-categories obtained by inverting (marked) unitary equivalences. We use this…

K-Theory and Homology · Mathematics 2019-09-16 Ulrich Bunke

We study the category pro-SSet of pro-simplicial sets, which arises in etale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-SSet so that it is possible to do homotopy theory in this category.…

Algebraic Topology · Mathematics 2007-05-23 Daniel C. Isaksen

We develop the theory of transfer and norm maps for finite group schemes, extending classical results from finite group theory to a context where induction and restriction are not necessarily bi-adjoint. In the additive setting, we…

Algebraic Geometry · Mathematics 2026-03-31 Kostas Karagiannis , Peter Symonds

Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…

Algebraic Topology · Mathematics 2007-05-23 Daniel Dugger

The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…

Representation Theory · Mathematics 2025-01-28 Xue-Song Lu , Pu Zhang

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

Logic · Mathematics 2021-01-01 Dakota Thor Ihli

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

Algebraic Topology · Mathematics 2009-09-06 Finnur Larusson

We derive a system of fixed-point equations for the equilibrium transfers in a class of one-to-one matching models with linear transferable utility. We then show that, when the degree of substitution between alternatives is bounded from…

General Economics · Economics 2025-07-09 Esben Scrivers Andersen

Explicit constructions for the minimal models of general and unimodular L-infinity algebra structures are given using the BV-formalism of mathematical physics and the perturbative expansions of integrals. In particular, the general formulas…

Quantum Algebra · Mathematics 2024-08-23 James Maunder

We construct and study a functorial extension of the evaluation map $S^1 \times \mathcal{L} X \to X$ to transfers along finite covers. For finite covers of classifying spaces of finite groups, we provide algebraic formulas for this…

Algebraic Topology · Mathematics 2021-08-17 Sune Precht Reeh , Tomer M. Schlank , Nathaniel Stapleton

We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then…

Algebraic Topology · Mathematics 2024-10-30 Martin Markl