Compact sheaves on a locally compact space
Copyright policy )Compact sheaves on a locally compact space
Let X X be a hypercomplete locally compact Hausdorff space and let C \mathcal C be a compactly generated stable ∞ \infty -category. We describe the compact objects in the ∞ \infty -category of C \mathcal C -valued sheaves S h v ( X , C ) Shv(X,\mathcal C) . When X X is a non-compact connected manifold and C \mathcal C is the unbounded derived ∞ \infty -category of a ring, our result recovers a result of Neeman. Furthermore, if C \mathcal C is a nontrivial compactly generated stable ∞ \infty -category, we show that S h v ( X , C ) Shv(X,\mathcal C) is compactly generated if and only if X X is totally disconnected.
- University of Copenhagen Denmark
Mathematics - K-Theory and Homology, Stable homotopy theory, spectra, FOS: Mathematics, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Algebraic Topology (math.AT), K-Theory and Homology (math.KT), Mathematics - Algebraic Topology
Mathematics - K-Theory and Homology, Stable homotopy theory, spectra, FOS: Mathematics, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Algebraic Topology (math.AT), K-Theory and Homology (math.KT), Mathematics - Algebraic Topology
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!