latex-pictures

 % This diagram represents the universal property of a projective limit
 % \varphojlim X_i, i.e. the fact the a projective limit is the limit of the
 % functor between I^op and the category of obejcts of the projective system
 % given my the projective system itself (for each index i it yields X_i and for
 % each inequality i <= j it yeilds \varphi_{i, j}
 % Copyright Pablo (C) 2021
 \begin{tikzpicture}[ampersand replacement=\&]
   % The objects
   \matrix(m)[matrix of math nodes,row sep=3em,column sep=3em,minimum width=2em]
   {     \&               X \&     \\
         \& \varprojlim X_i \&     \\
     X_i \&                 \& X_j \\};
 
   % The morphism
   \draw[->] (m-2-2) -- node[above right]{$\pi_j$} (m-3-3);
   \draw[->] (m-2-2) -- node[above left]{$\pi_i$} (m-3-1);
 
   % The projections
   \draw[dotted, ->] (m-1-2) -- node[right]{$\theta$} (m-2-2);
 
   % The arrow from the projective system
   \draw[->] (m-3-3) -- node[below]{$\phi_{i j}$} (m-3-1);
 
   % The arrows from the compatible family of morphisms
   \draw[->] (m-1-2) 
             to[relative, out=-30, in=-150] 
             node[left]{$\theta_i$}
             (m-3-1);
   \draw[->] (m-1-2) 
             to[relative, out=30, in=150] 
             node[right]{$\theta_j$}
             (m-3-3);
 \end{tikzpicture}