English
Related papers

Related papers: Homotopical Approach to Tensor Products of Modules

200 papers

We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…

Algebraic Topology · Mathematics 2020-03-09 Syunji Moriya

One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…

Category Theory · Mathematics 2025-11-24 Suddhasattwa Das

This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

q-alg · Mathematics 2008-02-03 Yi-Zhi Huang , James Lepowsky

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…

Category Theory · Mathematics 2014-02-26 Dave Benson , Srikanth B. Iyengar , Henning Krause

This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…

Algebraic Topology · Mathematics 2007-05-23 Mark Hovey

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…

Category Theory · Mathematics 2023-09-01 Sandra Mantovani , Mariano Messora , Enrico M. Vitale

Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines,…

History and Overview · Mathematics 2022-09-08 Andy Eskenazi , Kevin You , Will Vauclain , Robin Murugadoss

This is the first part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…

Algebraic Topology · Mathematics 2025-08-26 Jean-Paul Doeraene , Mohammed El Haouari

This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…

Category Theory · Mathematics 2026-03-02 Ismael Gutierrez Garcia , Luz Adriana Mejía Castaño

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

Quantum Algebra · Mathematics 2008-07-07 Yi-Zhi Huang , James Lepowsky , Lin Zhang

Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not on the nose. It was quickly realized that very little can be done with this information. Homotopy coherent category theory arose out of a desire to…

Category Theory · Mathematics 2023-01-12 Emily Riehl

This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…

Algebraic Topology · Mathematics 2020-08-13 Yuri Ximenes Martins

In the last year of his life, Bob Thomason reworked the notion of a model category, used to adapt homotopy theory to algebra, and used homotopy ends to affirmatively solve a problem raised by Grothendieck: find a notion of model structure…

Algebraic Topology · Mathematics 2016-08-17 Charles Weibel

This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…

Category Theory · Mathematics 2025-11-18 Daniel Almeida

Constructing and manipulating homotopy types from categorical input data has been an important theme in algebraic topology for decades. Every category gives rise to a `classifying space', the geometric realization of the nerve. Up to weak…

Algebraic Topology · Mathematics 2019-10-30 Stefan Schwede

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

History and Overview · Mathematics 2026-05-07 E. Alkin , O. Nikitenko , A. Skopenkov

We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…

High Energy Physics - Theory · Physics 2008-02-03 Yi-Zhi Huang , James Lepowsky

Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…

General Mathematics · Mathematics 2025-02-04 Skyler Marks

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

Quantum Algebra · Mathematics 2007-05-23 Yi-Zhi Huang , James Lepowsky , Lin Zhang
‹ Prev 1 2 3 10 Next ›