Hi @ch3600!
The functionality you’re after is possible to achieve but will require you to play about with HTML and basic PHP. If you’re comfortable with doing that, the very first step is for you to follow the guidance here to set up a child theme:
https://codex.www.ads-software.com/Child_Themes
If you’d like some more background about what child themes actually are and how they work, I recommend these resources:
https://www.smashingmagazine.com/2016/01/create-customize-wordpress-child-theme/
After you have created your child theme, duplicate the parent’s header.php file in your child theme’s directory.
Locate the following code in that file:
<?php if ( is_home() || is_front_page() || ( is_single() && 'image' == get_post_format() ) ) : ?>
<div class="featured-content">
<?php get_template_part( 'template-parts/loop', 'banner' ); ?>
</div>
<?php endif; ?>
The above code is telling the theme to display a banner at the top of any page it detects to be a home page or a single post with the image post format assigned to it.
You could make use of a conditional tag to expand the types of pages that this rule applies to.
For example, adding is_category() would add a banner to your category pages:
<?php if ( is_home() || is_front_page() || ( is_single() && 'image' == get_post_format() ) || is_category() ) : ?>
<div class="featured-content">
<?php get_template_part( 'template-parts/loop', 'banner' ); ?>
</div>
<?php endif; ?>
Next, duplicate the parent’s /template-parts/loop-banner.php file to your child theme’s directory.
In this file, we can see the type of banner that the theme displays for each type of page. If you’d like to change the type of banner that’s displayed on your category pages, this is where you can do it.
Let me know if that helps to point you in the right direction. If you let me know the URL of your site and how you’d like your category pages to look specifically, I can guide you further.