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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
95/2018

Flabby and injective objects in toposes

Ingo Blechschmidt

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.

Received:
Nov 14, 2018
Published:
Dec 6, 2018
MSC Codes:
18B25, 14F05
Keywords:
flabby objects

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Preprint
2018 Repository Open Access
Ingo Blechschmidt

Flabby and injective objects in toposes