Creating new factor column based on page range

I am looking for a smarter way to create a new factor column in an R data frame df. I have a dataframe, to which I would like to add a new column, which tells me, which section the given record belongs to. Sections like this:

section_in_text <- factor(c('Introduction', 'Characters', 'Footnotes', 'Bibliography'))

To which section a given record belongs is defined by the column df$page.

As of now, I have achieved this with a function, which looks like this:

document_sections <- function(x) {
if (x<5) {
return("Introduction")
}
else if ((5<=x) & (x<23)) {
return("Characters")
}...}

Then I have used sapply() df$section <- sapply(df$page, document_sections)

Is there maybe a smarter way to achieve the same result ?

Thanks.

Using cut():

df <- data.frame(page = seq(1, 40, by = 2))

df$section <- cut(
  df$page, 
  breaks = c(-Inf, 5, 23, 30, Inf),
  labels = c('Introduction', 'Characters', 'Footnotes', 'Bibliography'),
  right = FALSE
)

Or using dplyr::case_when():

library(dplyr)

df %>%
  mutate(section = factor(
    case_when(
      page < 5 ~ 'Introduction',
      page < 23 ~ 'Characters', 
      page < 30 ~ 'Footnotes', 
      !is.na(page) ~ 'Bibliography'
    ),
    levels = c('Introduction', 'Characters', 'Footnotes', 'Bibliography')
  ))

Result from either approach:

   page      section
1     1 Introduction
2     3 Introduction
3     5   Characters
4     7   Characters
5     9   Characters
6    11   Characters
7    13   Characters
8    15   Characters
9    17   Characters
10   19   Characters
11   21   Characters
12   23    Footnotes
13   25    Footnotes
14   27    Footnotes
15   29    Footnotes
16   31 Bibliography
17   33 Bibliography
18   35 Bibliography
19   37 Bibliography
20   39 Bibliography