Let us assume that we have exact sequence of vector spaces:
$$0\to U\to V\to W\to 0.$$
We can think of $0\to U\to V$ as a resolution of $W$.
Can we construct some canonical resolution of $\Lambda^n W$ in terms of some functors (like $\Lambda^ k U, S^l V$) of $U$ and $V$?
For example we have
$$U\otimes \Lambda^{n-1}V\to \Lambda^n V\to \Lambda^n W\to 0$$
is exact. Here the first map is multiplication ant the second is natural projection. Can we extend this sequence to the left?