$skuArray = array();
$categoryCollection = Mage::getModel('catalog/category')->getCollection();
foreach ($categoryCollection as $category) {
    $skuArray[$category->getId()] = $category->getProductCollection()->getColumnValues('sku');
}

$categoryCollection = Mage::getModel('catalog/category')->getCollection();
foreach ($categoryCollection as $category) {
    $skus = $category->getProductCollection()->getColumnValues('sku');
    $category->setData('skus', $skus);
}

foreach($categoryCollection as $category) {
    $categorySkus = $category->getData('skus');
}

$categories = Mage::getResourceModel('catalog/category_collection');
foreach ($categories as $category) {
    $products = $category->getProductCollection();
    foreach ($products as $product) {
        $sku[$product->getId()] = $product->getSku();
    }
}