Select a categorie in Collection

Hello,
I would like what this loop return only the category of the page.categories.
So I try this assign -> site.products[page.categories]
but no result. I don’t find a filter to do this condition

Thanks for and advice

 `---

layout: default

{{ page.categories | capitalize }}

    {% assign products = site.products[page.categories] %} {% for product in products %}
  • {{ product.name }} {% for cat_name in product.categories %} {{ cat_name }} {% endfor %}
  • {% else %}

    Error -- Product empty

    {% endfor %}
`