\documentclass{standalone}
\usepackage{tikz}
\usepackage{standalone}
\begin{document}
\begin{tikzpicture}[auto]

\node (a) at (1, 1) {$A$}; \node (b) at (-1,0) {$A$};
\node (c) at (1, 0) {$A \times A$};   \node (d) at (3, 0) {$A$};
\draw[->] (a) to node[swap] {$\scriptstyle \mathrm{id}_a$} (b);
\draw[->,dashed] (a) to node {$\scriptstyle \delta_a$} (c);
\draw[->] (a) to node {$\scriptstyle \mathrm{id}_a$} (d);
\draw[->] (c) to node {$\scriptstyle \pi_{1}$} (b);
\draw[->] (c) to node[swap] {$\scriptstyle \pi_{2}$} (d);

\node (e) at (7, 1) {$B$}; \node (f) at (5,0) {$B$};
\node (g) at (7, 0) {$B \sqcup B$};   \node (h) at (9, 0) {$B$};
\draw[->] (f) to node[swap] {$\scriptstyle \tau_1$} (g);
\draw[->] (h) to node {$\scriptstyle \tau_2$} (g);
\draw[->,dashed] (g) to node {$\scriptstyle \delta_b$} (e);
\draw[->] (f) to node {$\scriptstyle \mathrm{id}_b$} (e);
\draw[->] (h) to node[swap] {$\scriptstyle\mathrm{id}_b$} (e);
\end{tikzpicture}
\end{document}