%Sayyed Ahmad Mousavi

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{arrows}
\usepackage{amsmath}
\DeclareMathOperator{\Tor}{Tor}


\begin{document}

\begin{tikzcd}
  \cdots \rar   & \Tor_3^A(A, M) \rar & \Tor_3^A(K,M) \rar & \Tor_3^A(K/A,M)
          \ar[out=0, in=180, looseness=2, overlay]{dll}   & \\
        & \Tor_2^A(A, M) \rar & \Tor_2^A(K,M) \rar & \Tor_2^A(K/A,M)
          \ar[out=0, in=180, looseness=2, overlay]{dll}   & \\
        & \Tor_1^A(A, M) \rar & \Tor_1^A(K,M) \rar & \Tor_1^A(K/A,M)
          \ar[out=0, in=180, looseness=2, overlay]{dll}   & \\
        & A \otimes_A M  \rar & K \otimes_A M \rar & K/A\otimes_A M \rar & 0
\end{tikzcd}

\[
\begin{tikzcd} 
X \ar[-]{r} & Y \ar{r} & Z 
\end{tikzcd}
\]


\[
\begin{tikzcd}[column sep=small] 
&  
  (X_{0},x) 
  \arrow[hookrightarrow]{dr}{i'}
  \arrow[left hook->,swap]{dl}{i} % <-- reflect the direction of the hook
\\
(X,x)
  \arrow{dr} \arrow{rr} 
&&
(X', x)
  \arrow{dl} \\
&
(U,u)  
\end{tikzcd}
\]


\begin{figure}[!h]
     \centering
     \begin{tikzcd}[row sep=huge, column sep=huge, text height=1.5ex, text depth=0.25ex]
          \displaystyle\prod_{i=1}^{p} \arrow{r}{i} \arrow[bend right=50,shorten >=10pt]{rr}{T} & \mathcal{M} \arrow{r}{\pi} & \bigotimes\limits_{i=1}^{p}V_i
     \end{tikzcd}
\end{figure}
\end{document}