Exact Sequences - Diagrams that 'commute' - vertical arrows

[Math Amateur]

I am reading Dummit and Foote on Exact Sequences and some of the 'diagrams that commute' have vertical arrows.

Can someone please help me with the LaTex for these diagrams.

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

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

 

[Opalg]

$\mathcal{AMS}\TeX$ has a package amscd for typesetting commutative diagrams. It is not available with the Mathjax program used for TeX in this forum. But you can use the array environment to construct diagrams such as $\begin{array}{ccc} A & \stackrel{\alpha}{\longrightarrow} & B \\ \big\downarrow\vcenter{\rlap{\scriptsize\phi}} && \big\downarrow\vcenter{\rlap{\scriptsize\psi}} \\ C & \stackrel{\smash\beta}{\longrightarrow} & D \end{array}$.

\begin{array}{ccc} 
A & \stackrel{\alpha}{\longrightarrow} & B \\ 
\big\downarrow\vcenter{\rlap{\scriptsize\phi}} & & \big\downarrow\vcenter{\rlap{\scriptsize\psi}} \\ 
C & \stackrel{\smash\beta}{\longrightarrow} & D 
\end{array}

In that code, you can make the down arrows longer if you replace big by Big. (The commands \rlap and \smash are there to improve the spacing.)

 

[soroban]

Hello, Peter! Bernhard!

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

\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.