Column category path_published is a calculation of all parents and own category published.

I have experience with big joomla 3 website and a lots of time I try to improve performance.
This is one of that.

You can see performance improvement on featured or category view especially.
All calculation of category state is calculated when administrator change state of category.
Front end requests get one column to check - c.path_published.

Examples of category paths (after calculation):

• Root(published=1, path_published=1)->Category1(published=1, path_published=1)
  (... - represent about line)
• ... Category2(published=-2, path_published=-2)->Category3(published=1, path_published=-2)
• ... Category2(published=2, path_published=2)->Category3(published=1, path_published=2)
• ... Category2(published=0, path_published=0)->Category3(published=1, path_published=0)
• ... Category2(published=2, path_published=2)->Category3(published=0, path_published=0)
• ... Category2(published=2, path_published=2)->Category3(published=1, path_published=2)

Priority for calculation state of path_published:

• the most priority has Trash state (-2), all children will have -2
• the next is Unpublished (0), all children may have -2 or 0
• the next is Archive(2), all children may have -2,0 or 2
• the last one is Published (1)

Please comment.