latex code diagram

Question

It will be helpful if someone writes for me the code in latex for the following diagram and explain the code. The inverse limit is taken over s

Answer 1

This is a code that demonstrates two solutions: the psmatrix environment from pst-node (based on pstricks) and the tikz-cd environment from the homonymous package (based on tikz-pgf):

\documentclass[pdf]{article}
\usepackage{mathtools} 
 \usepackage{pst-node}
\usepackage{tikz-cd} 

\begin{document}
\texttt{psmatrix solution: }
 \[ \psset{arrows=->, arrowinset=0.25, linewidth=0.6pt, nodesep=3pt, rowsep=0.6cm, colsep = 1cm}
 \everypsbox{\scriptstyle}
 \begin{psmatrix}
%%% nodes
  0 & \varprojlim_{s} M/p^s & \varprojlim_{s} N/p^s & \varprojlim_{s} P/p^s& 0\\%
0 & M & N & P& 0
 %%% horizontal arrows
\ncline{1,1}{1,2} \ncline{1,2}{1,3} \ncline{1,3}{1,4} \ncline{1,4}{1,5}
 \ncline{2,1}{2,2} \ncline{2,2}{2,3} \ncline{2,3}{2,4} \ncline{2,4}{2,5}
 %%% vertical arrows
\psset{nodesepA = -5pt}
 \ncline{1,2}{2,2} \ncline{1,3}{2,3} \ncline{1,4}{2,4}
% \ncline[offset=0.8pt]{2,2}{3,2} \ncline[offset=-0.6pt]{2,3}{3,3}   \ncline[offset=0.6pt]{2,4}{3,4}
 \end{psmatrix}
 \]
\vskip 1cm

\texttt{tikz-cd solution: }
\[ \begin{tikzcd}\everymath{\displaystyle}
  0 \arrow{r}& \smash{\varprojlim\limits_{s}} M/p^s \arrow{r}\arrow{d}& \smash{\varprojlim\limits_{s} }N/p^s \arrow{r}\arrow{d} & \smash{\varprojlim\limits_{s}} P/p^s\arrow{r}\arrow{d}& 0\\%
0 \arrow{r}& M \arrow{r}& N\arrow{r} & P\arrow{r}& 0
\end{tikzcd}
\]

\end{document}