Vol. 25, No. 1, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Vol. 286: 1  2
Vol. 285: 1  2
Vol. 284: 1  2
Vol. 283: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Cosheaves and homology

Glen Eugene Bredon

Vol. 25 (1968), No. 1, 1–32
Abstract

In this paper we initiate a study of the theory of cosheaves of modules. We are interested mainly in those facts which are not encompassed by the known theories of sheaves with values in general categories. A central result is the establishment of the existence of a reasonably large subcategory of the category of precosheaves and a reflector from this to the subcategory of cosheaves. The general theory is applied to the study of the Čech, singular, and Borel-Moore homology theories. The main applications establish that the Čech and Borel-Moore homology theories coincide on locally compact and paracompact clc spaces and that the Čech and singular theories coincide on paracompact HLC spaces. These isomorphisms are established for locally constant coefficients. For constant coefficients the latter result was originally established by Mardešić and the former by O. Jussila. There are also applications to acyclic coverings and to mappings.

Mathematical Subject Classification
Primary: 55.32
Milestones
Received: 8 February 1967
Published: 1 April 1968
Authors
Glen Eugene Bredon