Preciso de muita ajuda para fazer com que este diagrama comutativo pareça apresentável. Estou brincando com isso há literalmente semanas e isso é o melhor que tenho.
A única supressão que eu poderia aceitar é trocar $H^{n-p}(F)$por uma supressão como $\mathcal{F}$. O código é:
\[\begin{tikzpicture}[scale=1.5]
\node (sa) at (0,5) {$\ldots$};
\node (sb) at (4,5) {$\ldots$};
\node (a1) at (0,4.3) {$\mathop\bigoplus\limits_{p = 0}^n [H^p(U\cup V) \otimes H^{n-p}(F)]$};
\node (a2-1) at (-.12,3.3) {$\mathop\bigoplus\limits_{p = 0}^n [(H^p(U)\otimes H^{n-p}(F)$};
\node (a2-2) at (0,3) {$\oplus$};
\node (a2-3) at (.16,2.7) {$(H^p(V)\otimes H^{n-p}(F))]$};
\node (a3) at (0,1.7) {$\mathop\bigoplus\limits_{p = 0}^n [H^p(U\cap V)\otimes H^{n-p}(F)]$};
\node (a4) at (0,.7) {$\mathop\bigoplus\limits_{p = 0}^n [H^{p+1}(U\cup V) \otimes H^{n-p}(F)]$};
\node (b1) at (4,4.3) {$H^n(\pi^{-1}(U\cup V))$};
\node (b2-1) at (4,3.3) {$H^n(U\times F)$};
\node (b2-2) at (4,3) {$\oplus$};
\node (b2-3) at (4,2.7) {$H^n(V\times F)$};
\node (b3) at (4,1.7) {$H^n((U\cap V\times F))$};
\node (b4) at (4,.7) {$H^{n+1}(\pi^{-1}(U\cup V))$};
\node (ea) at (0,0) {$\ldots$};
\node (eb) at (4,0) {$\ldots$};
\path[->,font=\scriptsize,>=latex]
([xshift=5pt]sa.east) edge node[above]{$\Psi$} ([xshift=-5pt]sb.west)
(a1) edge node[above]{$\Psi$} (b1)
([xshift= 36pt]a2-2.east) edge node[above]{$\Psi$} ([xshift= -20pt]b2-2.west)
(a3) edge node[above]{$\Psi$} (b3)
([xshift=5pt]ea.east) edge node[above]{$\Psi$} ([xshift=-5pt]eb.west)
(a4) edge node[above]{$\Psi$} (b4)
(sa) edge ([yshift= -3.6pt]a1.north)
([yshift=5pt]a1.south) edge node[left]{$\delta$} ([xshift= 3.43pt,yshift=-4pt]a2-1.north)
([xshift= -4.55pt]a2-3.south) edge node[left]{$\gamma$} ([yshift=-3.6pt]a3.north)
([yshift= 5pt]a3.south) edge node[left]{$d^*$} ([yshift= -3.6pt]a4.north)
([yshift= 5pt]a4.south) edge (ea)
(sb) edge (b1)
(b1) edge node[right]{$\delta$} (b2-1)
(b2-3) edge node[right]{$\gamma$} (b3)
(b3) edge node[right]{$d^*$} (b4)
(b4) edge (eb);
\end{tikzpicture}\]
Responder1
Aqui está uma possibilidade com tikz-cd; os rótulos Psi seriam melhor alinhados; ládeveseja um caminho!
\documentclass{article}
\usepackage{amsmath,mathtools}
\usepackage{tikz-cd}
\begin{document}
\[
\newcommand{\sbop}{\mathop{\textstyle\bigoplus}\limits}
\begin{tikzcd}[column sep=6em,row sep=large]
\cdots \arrow[r,"\Psi"] \arrow[d] & \cdots \arrow[d]
\\
\smash{\sbop_{p = 0}^n}\, [H^p(U\cup V) \otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d,swap,"\delta"]
& H^n(\pi^{-1}(U\cup V)) \arrow[d,"\delta"]
\\
\begin{multlined}
\smash[t]{\sbop_{p = 0}^n}\, [(H^p(U)\otimes H^{n-p}(F) \\
\oplus (H^p(V)\otimes H^{n-p}(F))]
\end{multlined}
\arrow[r,"\Psi"] \arrow[d,swap,"\gamma"]
& H^n(U\times F) \oplus H^n(V\times F) \arrow[d,"\gamma"]
\\
\smash{\sbop_{p = 0}^n}\, [H^p(U\cap V)\otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d,swap,"d^*"]
& H^n((U\cap V\times F)) \arrow[d,"d^*"]
\\
\smash{\sbop_{p = 0}^n}\, [H^{p+1}(U\cup V) \otimes H^{n-p}(F)]
\arrow[r,"\Psi"] \arrow[d]
& H^{n+1}(\pi^{-1}(U\cup V)) \arrow[d]
\\
\cdots \arrow[r,"\Psi"] & \cdots
\end{tikzcd}
\]
\end{document}
