2026-02-15 11:44:43
When I took the photo, I hadn't even realised that both were convertibles.
"Aber fassen wir es für den Moment vielleicht so zusammen: Wir haben in Deutschland ein sehr fein entwickeltes, aber nicht besonders gut austariertes System von Dingen, die man darf, und Dingen, die man nicht darf."
https://www.sueddeutsche.de/kultur/eisbachwelle-surfen-extremsport-drogen-selbstgefaehrdung-li.3370232
Higher algebra in $t$-structured tensor triangulated $\infty$-categories
Jiacheng Liang
https://arxiv.org/abs/2603.27786 https://arxiv.org/pdf/2603.27786 https://arxiv.org/html/2603.27786
arXiv:2603.27786v1 Announce Type: new
Abstract: We generalize fundamental notions of higher algebra, traditionally developed within the $\infty$-category of spectra, to the broader setting of $t$-structured tensor triangulated $\infty$-categories ($ttt$-$\infty$-categories). Under a natural structural condition, which we call "projective rigidity", we establish higher categorical analogues of Lazard's theorem and prove the existence and universal property of Cohn localizations. Furthermore, we generalize higher almost ring theory to the $ttt$-$\infty$-categorical setting, showing that $\pi_0$-epimorphic idempotent algebras are in natural bijection with idempotent ideals. By exploiting deformation theory, we establish a general \'etale rigidity theorem, proving that the $\infty$-category of \'etale algebras over a fixed connective base is completely determined by its discrete counterpart. Finally, we characterize the moduli of such projectively rigid $ttt$-$\infty$-categories, demonstrating that the presheaf $\infty$-category on the 1-dimensional framed cobordism $\infty$-category serves as the universal projectively rigid $ttt$-$\infty$-category.
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