Can a Sidebar Widget "Shadow" a Page from a Slider/Carousel?

Hello warriors

Can I have a given sidebar widget "shadow" a given image/page from a carousel/slider?

In other words - example; if the 4 options below represent the four different slider images
from my homepage, can a sidebar widget be made interdependent of, and for each one?
and therefore change depending upon which of the 4 selections is made?

Example:

goods1 goods2 goods3 goods4

When you select one of the 4 options; "goods1" of course, it takes you to
information about goods1, that's assumed - but can a sidebar widget be
shown that is exclusive to goods1? and the same true of "goods2?" again,
of course you would be taken to a page with more info about goods2, but
could it also display the sidebar widget specific to goods2? and so forth...


Or, is it not possible to govern the sidebar, and instead. I will have to
accept that it's contents will remain static, and cannot change to
accompany a given slider/carousel from the homepage?

(hope I did an adequate job of explaining)

The theme I'm using does not lend itself to any such "specific" controls.
But, is there a way to manipulate something in the general WP editor, or
perhaps within the (general) sidebar or widgets area, that will enable such
"shadowing?"

Is there a simple way to accomplish this?

(the general "pages and posts" inherent to WP themes, of course, still exist
- but the slider/carousel seems to be independent of their operation)

Your feedback is certainly appreciated

Danni~