drawing a specific diagram

Question

First of off: I have to say sorry for this dumb question. How to draw the diagram http://msp.org/pjm/1982/98-2/pjm-v98-n2-p15-s.pdf on page 6, which can be found in the proof of proposition 2.4 using tikzpicture or tikzcd and for documentclass{article}?

I have tried to follow instructions on several websites, and I have tried to modify examples like this http://texample.net/tikz/examples/commutative-diagram-tikz/ so far. I usually can do it by myself, but this time nothing works.

Greetings

Answer 1

You should think to the diagram as a three row and two column matrix. You add arrows in the cell where they start from, stating the target and the possible label.

In the present case, the label is \textstyle\cong; for it you specify "\textstyle\cong"'; the trailing apostrophe tells tikz-cd to place the label on the right side of the arrow: you should think to arrows like rivers, so you determine the right and left side by virtually placing yourself with the back to the source and the face to the end.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz-cd}

\begin{document}

\[
\begin{tikzcd}
K_*\varinjlim(A_\gamma)\otimes K_*(B) \arrow[r,dashed]
  & K_*((\varinjlim A_\gamma)\otimes B) \\
\varinjlim(K_*A_\gamma)\otimes K_*(B) \arrow[u,"\textstyle\cong"']
  & K_*(\varinjlim (A_\gamma\otimes B)) \arrow[u,"\textstyle\cong"']\\
\varinjlim((K_*A_\gamma)\otimes K_*(B)) \arrow[u,"\textstyle\cong"'] \arrow[r]
  & \varinjlim K_*(A_\gamma\otimes B)  \arrow[u,"\textstyle\cong"']
\end{tikzcd}
\]

\end{document}