Cubical Homotopy Theory And Monoidal Model Categories

Download or read book Cubical Homotopy Theory and Monoidal Model Categories written by Samuel Baruch Isaacson and published by . This book was released on 2009 with total page 308 pages. Available in PDF, EPUB and Kindle. 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.