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In the article exterior+algebra, in sect. 2, subsection In General, it says that the nth exterior power of an object $V$ is the cokernel of the antisymmetrization operator
$P_{A} = \frac{1}{n!} \sum_{\sigma \in S_{n}} \mathrm{sgn}(\sigma) \sigma.$Shouldn’t the exterior algebra be the image of this operator? If so, I am happy to edit the article accordingly.
It looks like in schur+functor what is used is the cokernel of $1 - P_A$ – is this correct?
Yes you’re correct. At least in the context of vector spaces over a field of characteristic $0$, $\Lambda^{n}V$ is the image of $P_A$, the coimage of $P_A$, the kernel of $1-P_A$ and the cokernel of $1-P_A$. So the statement at Schur functor is correct.
Great, thanks. I guess I’ll edit the article to bring it in line with Schur functor.
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