Universal homotopy theories
Daniel Dugger
Abstract
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 universal gadgets. The paper develops this formalism and discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes.
Create a lesson
Related papers
Constructive Bounds for the Topological Expressivity of Neural Networks
Kosio Beshkov
The (right) homotopy between two A∞-morphisms
Mattia Ornaghi
Reconstruction of graphs and surfaces from derived categories
Oscar Harr
Critical Point Theory for the Distance Function on PL-Spaces
Dirk Siersma
Derived plethystic algebra
Benjamin Antieau, Edith Hübner, Dmitry Kubrak et al.
The first homology of square-section braid groups
Minh Pham, Nicholas Wawrykow, Jacob Zweiback