So my theme doesn’t have a category.php file

First, if you are going to add to the theme, learn about Child Themes https://codex.wordpress.org/Child_Themes .

Then, create your own Category page – use a copy of one of the templates in your theme (placed in your Child Theme) and adjust the query to do a category-type query.

By creating a Child Theme, you ensure that any enhancements you make to the theme are not overwritten with a main theme update.

You might also be interested in the Template Hierarchy, which is how WP selects a template for various types of pages. Start here: https://developer.wordpress.org/themes/basics/template-hierarchy/ (within the Theme Handbook, also a great learning resource).

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