Lemma 6.27.2 (009B)—The Stacks project

Loading web-font TeX/Math/Italic

Table of contents
Part 1: Preliminaries
Chapter 6: Sheaves on Spaces
Section 6.27: Skyscraper sheaves and stalks
Lemma 6.27.2 (cite)

previous definition
next lemma

numberstags

history
statistics

Lemma 6.27.2. Let $X$ be a topological space, $x \in X$ a point, and $A$ a set. For any point $x' \in X$ the stalk of the skyscraper sheaf at $x$ with value $A$ at $x'$ is

$(i_{x, *}A)_{x'} = \left\{ \begin{matrix} A & \text{if} & x' \in \overline{\{ x\} } \\ \{ *\} & \text{if} & x' \not\in \overline{\{ x\} } \end{matrix} \right.$

A similar description holds for the case of abelian groups, algebraic structures and sheaves of modules.

Proof. Omitted. $\square$

Comments (0)

There are also:

1 comment(s) on Section 6.27: Skyscraper sheaves and stalks

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment