// Let's load the category Model and grab the product collection of that category
$product_collection = Mage::getModel('catalog/category')->load($categoryId)->getProductCollection();
// Now let's loop through the product collection and print the ID of every product
foreach($product_collection as $product) {
// Get the product ID
$product_id = $product->getId();
// Load the full product model based on the product ID
$full_product = Mage::getModel('catalog/product')->load($product_id);
// Now that we loaded the full product model, let's access all of it's data
// Let's get the Product Name
$product_name = $full_product->getName();
// Let's get the Product URL path
$product_url = $full_product->getProductUrl();
// Let's get the Product Image URL
$product_image_url = $full_product->getImageUrl();
// Let's print the product information we gathered and continue onto the next one
echo $product_name;
echo $product_image_url;
}