# Arrows in a commutative diagram

I would like to request assistance in adjusting the diagram as shown below, specifically to orientate the arrows on both the top and bottom lines of the 3rd square towards the left-hand side. I have attempted to implement changes using the provided code, however, it does not seem to produce the intended result. Any help in resolving this matter would be greatly appreciated. Thank you in advance.

    \begin{tikzcd}[column sep=large,row sep=large]
H^{3}(\mathbb S^{3}; \mathbb Z_2) \arrow[r, "\cong"] \arrow[d, "Sq^{2}"']
& H^{3}(\mathbb S^{3}\vee \mathbb S^{5}; \mathbb Z_2) \arrow[r, "\cong"]
\arrow[d, "Sq^{2}"']
& H^{3}(\Sigma\mathbb CP^{2}; \mathbb Z_2) \arrow[r, "\Sigma"] \arrow[d, "Sq^{2}"']
& H^{2}(\mathbb CP^{2}; \mathbb Z_2) \arrow[d, "Sq^{2}"] \\
H^{5}(\mathbb S^{3}; \mathbb Z_2) \arrow[r, ""]
& H^{5}(\mathbb S^{3}\vee \mathbb S^{5}; \mathbb Z_2) \arrow[r, "\cong"]
& H^{5}(\Sigma\mathbb CP^{2}; \mathbb Z_2) \arrow[r, "\Sigma"]
& H^{4}(\mathbb CP^{2}; \mathbb Z_2)
\end{tikzcd}


## 1 Answer

• Use \arrow[l] for left-pointing arrows (but place them in the rightmost cells)
• Use "<label>"' to swap the label to the opposite side
• Use \DeclareMathOperator to get the upright shape for pr and Sq
• Use braces {...} with \mathbb

\documentclass{article}

\usepackage{tikz-cd, amssymb, amsmath}
\DeclareMathOperator{\Sq}{Sq}
\DeclareMathOperator{\pr}{pr}

\begin{document}

\begin{tikzcd}[column sep=large,row sep=large]
H^{3}(\mathbb{S}^{3}; \mathbb{Z}_2) \arrow[r, "\cong"', "\pr^*"] \arrow[d, "\Sq^{2}"']
& H^{3}(\mathbb{S}^{3}\vee \mathbb{S}^{5}; \mathbb{Z}_2) \arrow[r, "\cong"'] \arrow[d, "\Sq^{2}"]
& H^{3}(\Sigma\mathbb{CP}^{2}; \mathbb{Z}_2) \arrow[d, "\Sq^{2}"]
& H^{2}(\mathbb{CP}^{2}; \mathbb{Z}_2) \arrow[d, "\Sq^{2}"] \arrow[l, "\Sigma"', "\cong"] \\
H^{5}(\mathbb{S}^{3}; \mathbb{Z}_2) \arrow[r, "\pr^*"']
& H^{5}(\mathbb{S}^{3}\vee \mathbb{S}^{5}; \mathbb{Z}_2) \arrow[r, "\cong"]
& H^{5}(\Sigma\mathbb{CP}^{2}; \mathbb{Z}_2)
& H^{4}(\mathbb{CP}^{2}; \mathbb{Z}_2) \arrow[l, "\Sigma", "\cong"']
\end{tikzcd}

\end{document}

• I'm not sure why you didn't fix all cases of \mathbb{<letter>}. Commented Mar 29, 2023 at 22:55
• @egreg: I thought I did. Looks like I missed two. Fixed now. Thanks. Commented Mar 30, 2023 at 13:55