https://pzhou.org/ 2026-08-18T04:34:49+00:00 https://pzhou.org/ https://pzhou.org/lib/tpl/dokuwiki/images/favicon.ico text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/questions/descent-via-localization?rev=1687708402&do=diff Descent via Localization What does descent mean? I was telling my linear algebra student the following example: suppose you have a linear map $f: V \to W$, and there is a subspace $V' \In V$ such that $f|_{V'}=0$, then $f$ descent to $V/V'$. In general, it means you define something on a 'cover' of an object, and you want to obtain the thing on the object itself. text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/questions/group-acts-on-a-category?rev=1687708402&do=diff Finite Group acts on a category Let $C$ be a category, $G$ be a finite group. For each $g \in G$, suppose we have a functor $[g]: C \to C$, such that there are natural equivalences $[g_1] [g_2] \xto{\cong} [g_1 g_2]$, satisfying associativity condition. Then, we can call this a text/html 2023-06-25T15:53:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://pzhou.org/questions/start?rev=1687708402&do=diff Questions