Multiline texts with braces in an equation

Question

I'm trying to type the equation

I tried the following with an error message:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{align}
  \left\lbrace
  \begin{align*}
  \textrm{$R$-bilinear maps}\\
  \varphi:M\times N\to L
  \end{align*}
  \right\rbrace \longleftrightarrow \left\lbrace
 \begin{align*}
  \textrm{$R$-module homomorphisms}\\
  \Phi:M\otimes_RN\to L
  \end{align*}
  \right\rbrace
\end{align}
\end{document}

How can I fix it?

Answer 1

I would use a very simpler code:

\documentclass[11pt,a4paper]{report}
\usepackage{amsmath}

\begin{document}
\[
\begin{Bmatrix}
    \textrm{$R$-bilinear maps}\\
    \varphi:M\times N\to L
\end{Bmatrix}
\longleftrightarrow
\begin{Bmatrix}
    \textrm{$R$-module homomorphisms}\\
    \Phi:M\otimes_RN\to L
\end{Bmatrix}
\]
\end{document}

Answer 2

The stack equivalent of Sigur's answer, using \braceVectorstack{}.

\documentclass[11pt,a4paper]{report}
\usepackage{amsmath}
\usepackage[usestackEOL]{stackengine}
\stackMath
\begin{document}
\[
\braceVectorstack{
    \textrm{$R$-bilinear maps}\\
    \varphi:M\times N\to L
}
\longleftrightarrow
\braceVectorstack{
    \textrm{$R$-module homomorphisms}\\
    \Phi:M\otimes_RN\to L
}
\]
\end{document}