How to setup menu data in Context_processor in Django?

Question

I have category and subcategory store in my database, and subcategory is related to category, I have multiple pages on my website, but I am able to display category in the menu on some pages, but I want to display on all pages, so I found the solution using context_processor, but I am unable to render HTML file there, it only takes data in the dictionary file, please check my code and let me know where I am mistaking.

here is my models.py file...

class Category(models.Model):
   cat_name=models.CharField(max_length=225)
   cat_slug=models.SlugField(max_length=225, unique=True)
   
   def __str__(self):
   return self.cat_name

class SubCategory(models.Model):
   subcat_name=models.CharField(max_length=225)
   subcat_slug=models.SlugField(max_length=225, unique=True)
   category = models.ForeignKey('Category', related_name='subcategoryies', on_delete=models.CASCADE, blank=True, null=True)
  
   def __str__(self):
   return self.subcat_name

here is my context_processor.py file...

from django.shortcuts import render
from dashboard.models import Category, SubCategory

def context_categories(request, cat_slug):
    category = Category.objects.all().order_by('-created_at')
    return render(request, "base.html", {'category':category})

included this file in settings.py file under TEMPLATES section

 'mainpage.context_processors.context_categories',

here is my base.html file...

{% for cat in category %}
      <li>
       <a href="javascript:void()">{{cat.cat_name}}</a>
          <ul>
           {% for subcat in cat.subcategoryies.all %}
            <li><a href="/subcategory/{{subcat.subcat_slug}}">{{subcat.subcat_name}}</a></li>
             {% endfor %}
           </ul>
       </li>
 {% endfor %}