That category page with the products inside is:
woocommerce >> templates >> content-product.php
And you can find that only function to show the Title inside this page as:
<h3><?php the_title(); ?></h3>
After that line you can add your own lines:
<br /><?php echo $product->get_sku(); ?> <br /><?php echo apply_filters( 'woocommerce_short_description', $post->post_excerpt ) ?>
These will display the SKU and the short-description of the product.
Btw, this is just a quick hard-coded method, you can try to add these functions to the hook on that page in your theme's functions.php.
add_action('woocommerce_after_shop_loop_item_title','woocommerce_template_single_excerpt', 5);
As it is mentioned in that hooks comments section that the PRICE is already hooked in there.
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