Closed Model Categories for Presheaves of Simplicial Groupoids and Presheaves of 2-Groupoids

2003/01/06 by Luo, Zhi-Ming, Bubenik, Peter, Kim, Peter T.
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0301045

Abstract

It is shown that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. Furthermore, their homotopy categories are equivalent to the homotopy categories of simplicial presheaves and homotopy 2-types, respectively.

Related

• Homotopy theory of presheaves of simplicial groupoids
• Groupoidal 2-quasi-categories and homotopy 2-types
• A model structure on the category of small categories for coverings
• Presheaves of groupoids as models for homotopy types
• A Quillen model category structure on some categories of comonoids