Dplyr applying a calculation on values in a grouping comparing each item to all _other_ items in the group

I want to work out whether a value in a grouping is different enough from other values in a grouping. Specifically I want to work out whether an end time of a matches with the start time of another lesson on the same day for the same student. Using diamonds, this is the equivalent code:

library(ggplot2)
diamonds %>% group_by(color, cut) %>% 
  mutate(clash = sum(
           lapply(
             diamonds %>% 
               filter(color == color, cut == cut, carat != carat) %$% carat,
             function(x) ifelse(x < carat - 0.01 && x > carat + 0.01, 1, 0)))) %>%
  arrange(color, cut, clash)

The plan is if clash is over 1, then I know that another diamond is very close in carat size to the diamond in that grouping. This gives me the following error:

Error in sum(sapply(diamonds %>% filter(color == color, cut == cut, carat !=  : 
  invalid 'type' (list) of argument

This makes the second call to diamond look dodgy