The Local Joyal Model Structure
Nicholas Meadows
TL;DR
This paper extends the Joyal quasi-category model structure from simplicial sets to simplicial presheaves, establishing a local model structure where weak equivalences are stalkwise Joyal equivalences.
Contribution
It introduces a new local model structure on simplicial presheaves based on the Joyal model, broadening its applicability.
Findings
The model structure on simplicial presheaves is established.
Weak equivalences are characterized as local Joyal equivalences.
The extension preserves key properties of the original Joyal model.
Abstract
It is shown that the Joyal quasi-category model structure for simplicial sets extends to a model structure on simplicial presheaves, for which the weak equivalences are local (or stalkwise) Joyal equivalences.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Nonlinear Waves and Solitons · Topological and Geometric Data Analysis