The Galois groupoid of G-spectra is equivalent to the étale fundamental groupoid of the Burnside ring of G.
Naturality of the infinity-categorical enriched Yoneda embedding , volume=
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Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.
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The Galois theory of $G$-spectra and the Burnside ring
The Galois groupoid of G-spectra is equivalent to the étale fundamental groupoid of the Burnside ring of G.
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Smooth categories in a 6 functor formalism and compact generation for nuclear categories in analytic geometry
Proves equivalence between smoothness of a rigid analytic variety and smoothness of its nuclear sheaves category in a six-functor formalism, relates compact generation to algebraization, and gives an example of a non-atomically generated internally smooth category.