The Minimum Theme for the Genesis Theme Framework includes a custom post type to create a portfolio. If you would like to create categories for that portfolio, you can create a custom taxonomy. Following this tutorial, will give you a method of categorizing your portfolio images.

Step 1: Find the following code in your functions.php file:

/** Create portfolio custom post type */
add_action( 'init', 'minimum_portfolio_post_type' );
function minimum_portfolio_post_type() {
	register_post_type( 'portfolio',
		array(
			'labels' => array(
				'name' => __( 'Portfolio', 'minimum' ),
				'singular_name' => __( 'Portfolio', 'minimum' ),
			),
			'exclude_from_search' => true,
			'has_archive' => true,
			'hierarchical' => true,
			'menu_icon' => get_stylesheet_directory_uri() . '/images/icons/portfolio.png',
			'public' => true,
			'rewrite' => array( 'slug' => 'portfolio' ),
			'supports' => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'trackbacks', 'custom-fields', 'comments', 'revisions', 'page-attributes', 'genesis-seo' ),
		)
	);
}

Step 2: Replace that code with this:

/** Create portfolio custom post type */
add_action( 'init', 'minimum_portfolio_post_type' );
function minimum_portfolio_post_type() {
	register_post_type( 'portfolio',
		array(
			'labels' => array(
				'name' => __( 'Portfolio', 'minimum' ),
				'singular_name' => __( 'Portfolio', 'minimum' ),
			),			
			'has_archive' => true,
			'hierarchical' => true,
			'menu_icon' => get_stylesheet_directory_uri() . '/images/icons/portfolio.png',
			'public' => true,
			'rewrite' => array( 'slug' => 'portfolio' ),
			'taxonomies' => array( 'portfolio-type' ),
			'supports' => array( 'title', 'editor', 'author', 'thumbnail', 'excerpt', 'trackbacks', 'custom-fields', 'comments', 'revisions', 'page-attributes', 'genesis-seo' ),
		)
	);
}

/* Register Portfolio Taxonomy */
add_action( 'init', 'create_portfolio_tax' );
function create_portfolio_tax() {
	register_taxonomy(
		'portfolio-type',
		'portfolio',
		array(
			'label' => __( 'Type' ),
			'hierarchical' => true
		)
	);
}

Step 3: Copy the archive-portfolio.php template from the child theme folder and save it as taxonomy-portfolio-type.php

Step4: Go to Settings > Permalinks and resave

Step 5: Go categorize some portfolio images! Then view your category at http://yoururl.com/portfolio-type/category-slug/