color node based on category in tanglegram

Question

I am trying to build a tanglegram using dendextra and ggdendro but I can't color nodes based on the category column in tanglegram. Please advise.

d1 <- c(1:5)
cate <- c("cat1", "cat2", "cat3", "cat1", "cat1")
d1 <- data.frame(d1, cate)

d2 <- c(1:5)
cate <- c("cat2", "cat3", "cat3", "cat1", "cat1")
d2 <- data.frame(d2, cate)

e1 <- dist(d1$d1)
e1 <- hclust(e1, method = "average")
dend <- as.dendrogram(e1)

f1 <- dist(d2$d2)
f1 <- hclust(f1, method = "average")
dend2 <- as.dendrogram(f1)

t <- dendlist(dend, dend2)
tanglegram(t, fast = TRUE) %>% set("nodes_col", (d1$cate))