Is it possible to show posts from one site in another site's category page?

Do you want to cross-post — have the post appear in both places as if they were always posted there?

This would be only for category pages, featured image, title, link and excerpt. From one blog to another, one way.

It can be done in a few different ways, depending on how you want to handle it.

Broadcast a post/page to other blogs. Whitelist, blacklist, groups and automatic category+tag posting/creation available.
* https://www.ads-software.com/extend/plugins/threewp-broadcast/

Allows you to duplicate posts and pages to multiple sub-blogs at once.
* https://www.ads-software.com/extend/plugins/multipost-mu/

Aggregate ALL posts on the network to one master site
* https://www.ads-software.com/extend/plugins/wordpress-mu-sitewide-tags/