This post could just as easily be called 'how to filter a WordPress category page by keyword search term'!
Anyway here is a standard WordPress search page URL (in this case for the keyword 'count'). It shows results from all categories:
And here is a WordPress category page URL (for the category 'web development'). It shows all posts in that category:
It is possible to combine the two. So the following URL only shows posts within the 'web development' category that also include the word 'count':
It is also possible to use the category ID in the URL instead and get the same results:
I recently used this technique on a client's classifieds website to generate quite specific browse pages in lieu of having a complex taxonomy.