R: calculate number of distinct categories in the specified time frame

here's some dummy data:

  user_id       date category
       27 2016-01-01    apple
       27 2016-01-03    apple
       27 2016-01-05     pear
       27 2016-01-07     plum
       27 2016-01-10    apple
       27 2016-01-14     pear
       27 2016-01-16     plum
       11 2016-01-01    apple
       11 2016-01-03     pear
       11 2016-01-05     pear
       11 2016-01-07     pear
       11 2016-01-10    apple
       11 2016-01-14    apple
       11 2016-01-16    apple

I'd like to calculate for each user_id the number of distinct categories in the specified time period (e.g. in the past 7, 14 days), including the current order

The solution would look like this:

 user_id       date category distinct_7 distinct_14
      27 2016-01-01    apple          1           1
      27 2016-01-03    apple          1           1
      27 2016-01-05     pear          2           2
      27 2016-01-07     plum          3           3
      27 2016-01-10    apple          3           3
      27 2016-01-14     pear          3           3
      27 2016-01-16     plum          3           3
      11 2016-01-01    apple          1           1
      11 2016-01-03     pear          2           2
      11 2016-01-05     pear          2           2
      11 2016-01-07     pear          2           2
      11 2016-01-10    apple          2           2
      11 2016-01-14    apple          2           2
      11 2016-01-16    apple          1           2

I posted similar questions here or here, however none of it referred to counting cumulative unique values for the specified time period. Thanks a lot for your help!