Flabby and injective objects in toposes
Category Theory
2018-10-31 v1
Abstract
We introduce a general notion of flabby objects in elementary toposes and study their basic properties. In the special case of localic toposes, this notion reduces to the common notion of flabby sheaves, yielding a site-independent characterization of flabby sheaves. Continuing a line of research started by Roswitha Harting, we use flabby objects to show that an internal notion of injective objects coincides with the corresponding external notion, in stark contrast with the situation for projective objects. We show as an application that higher direct images can be understood as internal cohomology, and we study flabby objects in the effective topos.
Cite
@article{arxiv.1810.12708,
title = {Flabby and injective objects in toposes},
author = {Ingo Blechschmidt},
journal= {arXiv preprint arXiv:1810.12708},
year = {2018}
}
Comments
17 pages