Create the block file in your module.

<?php
namespace MagemonkeyCategoryBlock;
 
class Category extends MagentoFrameworkViewElementTemplate
{
    public function __construct(
        MagentoFrameworkViewElementTemplateContext $context,
        MagentoCatalogApiCategoryRepositoryInterface $categoryRepository,
        array $data = []
    ) {
        $this->categoryRepository = $categoryRepository;
        parent::__construct($context, $data);
    }
 
    /* $categoryId as category id */
    public function getCategoryById($categoryId){
        try {
            return $category = $this->categoryRepository->get($categoryId);
        } catch (MagentoFrameworkExceptionNoSuchEntityException $e) {
            return ['response' => 'Category Not Found'];
        }
    }
}
?>

Put this code in your template file and pass the category id in getCategoryById function.

<?php  
$categoryId = 10; // category id
$getCategory = $block->getCategoryById($categoryId);
echo $getCategory->getName();echo "<br>";
echo $getCategory->getUrlKey();echo "<br>";
echo $getCategory->getIsActive();echo "<br>";
echo "<pre>";print_r($getCategory->getData()); ?>