Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-11T00:43:17.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypercovers and simplicial presheaves

Published online by Cambridge University Press:  15 January 2004

DANIEL DUGGER ,
SHARON HOLLANDER  and
DANIEL C. ISAKSEN
DANIEL DUGGER
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A. e-mail: [email protected]
SHARON HOLLANDER
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A. e-mail: [email protected]
DANIEL C. ISAKSEN
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, U.S.A. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We use hypercovers to study the homotopy theory of simplicial presheaves. The main result says that model structures for simplicial presheaves involving local weak equivalences can be constructed by localizing at the hypercovers. One consequence is that the fibrant objects can be explicitly described in terms of a hypercover descent condition, and the fibrations can be described by a relative descent condition. We give a few applications for this new description of the homotopy theory of simplicial presheaves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 136 , Issue 1 , January 2004 , pp. 9 - 51
Copyright
2004 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)