Cubical Homotopy Theory and Monoidal Model Categories
Author | : Samuel Baruch Isaacson |
Publisher | : |
Total Pages | : 308 |
Release | : 2009 |
ISBN-10 | : OCLC:467778552 |
ISBN-13 | : |
Rating | : 4/5 (52 Downloads) |
Book excerpt: Suppose [Special characters omitted.] is a combinatorial symmetric monoidal model category. Dan Dugger has shown that [Special characters omitted.] may be realized as a left Bousfield localization of the projective model structure on simplicial presheaves on a small site. However, if [Special characters omitted.] is not already simplicially enriched, this presentation will not respect the monoidal structure of [Special characters omitted.] . In this paper we will construct a symmetric cubical site [Special characters omitted.] extending the classical cubical site. By replacing the category of simplicial sets with the category of presheaves of sets over [Special characters omitted.] we can use Dugger's methods to produce a presentation of [Special characters omitted.] as presheaves of spaces on a monoidal site retaining the monoidal structure in [Special characters omitted.] as the convolution product.