# Exact Sequences - Diagrams that 'commute' - vertical arrows

• Aug 17th 2013, 04:30 PM
Bernhard
Exact Sequences - Diagrams that 'commute' - vertical arrows
I am reading Dummit and Foote on Exact Sequences and some of the 'diagrams that commute' have vertical arrows.

I have given an example in the attachment "Exact Sequences - Diagrams with Vertical Arrows" - where I also frame my question (please see attachement)

I have also attached Dummit and Foote Section 10.5 page 381 which has two examples of the diagrams to which I refer.

Would be very grateful for help.

Peter
• Aug 17th 2013, 08:53 PM
Soroban
Re: Exact Sequences - Diagrams that 'commute' - vertical arrows
Hello, Bernhard!

Here's one way . . .

$\begin{array}{ccccccccc} &&& \alpha && \beta && \gamma \\ O & \to & A & \to & B & \to & C & \to & O \\ && \quad\downarrow \phi && \quad\downarrow\psi && \quad\downarrow\tau \\ O & \to & A' & \to & B' & \to & C' & \to & O \end{array}$

Code:

\begin{array}{ccccccccc} &&& \alpha && \beta && \gamma \\ O & \to & A & \to & B & \to & C & \to & O \\ && \quad\downarrow \phi && \quad\downarrow\psi && \quad\downarrow\tau \\ O & \to & A' & \to & B' & \to & C' & \to & O \end{array}
Note: You may have to type all this in one continuous line.