Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids
نویسنده
چکیده
We prove that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. We also show that the homotopy categories associated to the two categories are equivalent to the homotopy categories of simplicial presheaves and homotopy 2-types, respectively.
منابع مشابه
Diagrams Indexed by Grothendieck Constructions and Stacks on Stacks
Let I be a small indexing category, G : I → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on BG and the category of I-diagrams over N(G) (resp. G). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (re...
متن کاملDiagrams Indexed by Grothendieck Constructions
Let I be a small indexing category, G : I → Cat be a functor and BG ∈ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicial sets (resp. categories) indexed on BG and the category of I-diagrams over N(G) (resp. G). As an application we obtain a Quillen equivalence between the categories of presheaves of simplicial sets (re...
متن کاملON THE HOMOTOPY THEORY OF n-TYPES
We achieve a classification of n-types of simplicial presheaves in terms of (n− 1)-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we obtain a good homotopy theory of (weak) higher groupoids.
متن کاملMorita Theory for Hopf Algebroids and Presheaves of Groupoids
Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff , the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasi-coherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of preshe...
متن کاملHomotopy classification of gerbes
Gerbes are locally connected presheaves of groupoids on a small Grothendieck site C. Gerbes are classified up to local weak equivalence by path components of a cocycle category taking values in the diagram Grp(C) of 2-groupoids consisting of all sheaves of groups, their isomorphisms and homotopies. If F is a full subpresheaf of Grp(C) then the set [∗, BF ] of morphisms in the homotopy category ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009