Improve Search Engine

The search engine will only search within the posts, but did not find anything when I search directly the “Categories” or “Sub-Categories”. Just find exact words but not similar words, and so within the publications. Please tell me how could I do to fix this?

Let me also look at the result of what is inside the categories or subcategories without the need to write the word. ex:

Category: Dog – Subcategory: Little Dog

For me to understand better ….. When looking for a Subcategory eg “Dogs”, tells me 0 results.
I want to write: “Dogs” in “all categories” and show me the result of what’s inside that category or subcategory.

Example 2:

Bad:
Im search in “All Categories” ——– “Dogs” = 0 Results
(but i have subcategory “Dogs”!!!)

Correct:
Im search in “All Categorias” ——— “Dogs” = all results, included all inside all categories (and included sub-C.)

I understand!? You can help me with this please? It is very important to me.