Geometric (∞,1)-categories are introduced with (hyper)sheaves characterized by Čech descent; applications include identifying topologies on (n,1)-topoi and equivalences for truncated sheaves.
Tensor triangular geometry of filtered objects and sheaves , ISSN=
3 Pith papers cite this work. Polarity classification is still indexing.
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The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
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On Galois categories and condensed contractible schemes
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.