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Flabby and injective objects in toposes

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arxiv 1810.12708 v1 pith:35U35Q5F submitted 2018-10-30 math.CT

Ingo Blechschmidt This is my paper · ORCID
classification math.CT
keywords flabbyobjectsnotiontoposesinjectiveinternalsheavesapplication
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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.

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  1. Logic and Concepts in the 2-category of Topoi

    math.LO 2025-04 conditional novelty 7.0 of 10

    Kan injectivity yields a uniform framework for fragments of geometric logic, each with an associated lax-idempotent pseudomonad and classifying topos.

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