questions:start
Questions
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 group acting on a category.
Is this picture enough?
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.
questions/start.txt · Last modified: 2023/06/25 15:53 by 127.0.0.1