Sorry for my bad english...
I want to create a tree with matherials using category as items and matherial items as items
In category i write header, full description and then i whant to add comments
below are subcategories headers.

it need me as real SEO structure. For example /tables(about tables)/red(about red tables)/buy(how to buy red tables).
"Tables", "Red tables" and "Buy red tables" i need to set comments.

Hello Evgeny,

If I understood correctly, by default the category cannot handle comments. You need to use a 3rd party extension or manually integrate a service like Disqus

is - solution to the problem, but i want to authentify users on my site and save user comments on my site

Disqus will save it on their service, not your database neither will Facebook comments.
However in the JED and getk2.org/extend/ are several commenting extensions.

I checked all extensions in JED.
none work in categories

And here Russian Yandex search engine not indexing disqus....

Disqus is being rendered inside an iframe, so this is why it is not rendered. You can also check FB comments. There are also several other commenting services you can try.

Yes in Russia we have a analog of FB - Vkontakte. It has comments, but users older than 40 years not have accounts on it.
Can you say me - what php files i must to edit in K2 and where in database comments are saving.
how can i invoke comments component form in k2 category php template for example.
If i do that then I 'll write here about it.

I would suggest instead of hacking K2's code which will result in undesired effects, developing a K2 plugin.

You can find an example here: getk2.org/extend/extensions/90-example-k2-plugin-for-developers