https://ou-liu-red-sugar.github.io/tags/presentable-category/Recent content in Presentable Category on Ou LiuHugo -- 0.146.0en-usMon, 29 Dec 2025 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/gestalten/presentable-categories/Sun, 28 Dec 2025 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/gestalten/presentable-categories/This note reviews the basic theory of presentable categories. We focus on κ-compact objects, Ind-completions, accessible categories, and their role in organizing large categories via filtered colimits.https://ou-liu-red-sugar.github.io/notes/notes/gestalten/presentable-n-categories/Mon, 29 Dec 2025 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/gestalten/presentable-n-categories/This note introduces the notion of presentable n-categories.https://ou-liu-red-sugar.github.io/notes/notes/gestalten/stefanich-rings/Mon, 29 Dec 2025 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/gestalten/stefanich-rings/This note discusses the colimit of the sequence \[ \mathsf{CAlg}(1\mathsf{Pr}) \hookrightarrow \mathsf{CAlg}(2\mathsf{Pr}) \hookrightarrow \cdots \hookrightarrow \mathsf{CAlg}(n\mathsf{Pr}) \hookrightarrow \cdots . \] in $1\mathsf{Pr}$, and discuss the $n$-affine, $n$-proper, $n$-suave and $n$-prim maps.https://ou-liu-red-sugar.github.io/notes/notes/gestalten/everything-becomes-affine-under-sufficient-categorification/Mon, 29 Dec 2025 00:00:00 +0000https://ou-liu-red-sugar.github.io/notes/notes/gestalten/everything-becomes-affine-under-sufficient-categorification/This note constructs the six-functor formalism on \(n\mathsf{Pr}_{(-)}\), shows that it is sheafy with respect to fpqc topology, and then extends the theory from affine schemes of derived rings to stacks.