How to put the Category title?

I have this Website https://www.todosobreseriestv.com/ and i want to put the category name in the title space of the browser.

For now, I’ve done that with success inserting this code: <?php while (have_posts()) : the_post(); ?><?php the_title(); ?><?php endwhile; ?> -- ?<?php bloginfo('name'); ?>? on the page.php and single.php

So with this code when i open a page or a single post in the browser title puts the name of the post/page and after the name of the website.

I don’t have a category.php so the code must be changed from index.php.

I tried to do some modifications but the results are not good enough. So can some one help me? Thanks