https://ou-liu-red-sugar.github.io/tags/six-functor-formalism/Recent content in Six Functor Formalism on Ou LiuHugo -- 0.146.0en-usFri, 24 Apr 2026 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/a-brief-introduction-to-6-functor-formalisms/Fri, 24 Apr 2026 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/a-brief-introduction-to-6-functor-formalisms/A coherent pass through six-functor formalisms. From the structural properties one wants of cohomology, through the Liu–Zheng / Mann / Scholze span-category packaging and the Cnossen–Lenz–Linskens universal property, to Scholze's organising observation: Poincaré duality for a morphism is *precisely* a dualizability statement in the $2$-category of kernels. We close with Heyer–Mann's suave/prim weakening, Aoki's one-step étale/proper picture, and transmutation to Gestalten.