RunPCA scope in Seurat v5

[rbutleriii]

So I went through the tutorial on integration in Seurat v5 and I had a question about the scope of RunPCA with the layers format. So in the tutorial, RunPCA is run after splitting the counts into layers, but is then used to generate an unintegrated UMAP including all cells in all layers (each having their own scale.data). It isn't rerun again, so I am wondering if it is calculated separately for each layer separately and stored in a single reduction slot?

The main reason for asking is after joining the layers together later on, I would think you would have to re-run RunPCA if you wanted to do some unified follow-up analysis that relies on the pca reduction. But is the pca reduction the same whether the layers are joined or not (i.e. you wouldn't have to re-run RunPCA)?