Lemma 42.68.7. Let $(R, \mathfrak m, \kappa )$ be any local ring. The functor

\[ \det \nolimits _\kappa : \left\{ \begin{matrix} \text{finite length }R\text{-modules}
\\ \text{with isomorphisms}
\end{matrix} \right\} \longrightarrow \left\{ \begin{matrix} 1\text{-dimensional }\kappa \text{-vector spaces}
\\ \text{with isomorphisms}
\end{matrix} \right\} \]

endowed with the maps $\gamma _{K \to L \to M}$ is characterized by the following properties

## Comments (0)