I am trying to understand a proof where there are graded algebras and inverse limit involved.
In one of the steps it seems to commute this two elements. Is there any reference where this is stated.
$$\varprojlim (gr(\Lambda^*_n))=gr(\varprojlim \Lambda_n^*).$$
Where $\Lambda^*_n$ stands for the shifted symmetric polynomials of $n$ indeterminates.
Note that the inverse limit $\varprojlim \Lambda_n^* = \Lambda^*$ is taken in the category of filtered algebras.