Source

File: wp-includes/category.php

function get_category_by_path( $category_path, $full_match = true, $output = OBJECT ) {
	$category_path  = rawurlencode( urldecode( $category_path ) );
	$category_path  = str_replace( '%2F', '/', $category_path );
	$category_path  = str_replace( '%20', ' ', $category_path );
	$category_paths = '/' . trim( $category_path, '/' );
	$leaf_path      = sanitize_title( basename( $category_paths ) );
	$category_paths = explode( '/', $category_paths );
	$full_path      = '';

	foreach ( (array) $category_paths as $pathdir ) {
		$full_path .= ( '' !== $pathdir ? '/' : '' ) . sanitize_title( $pathdir );
	}

	$categories = get_terms(
		array(
			'taxonomy' => 'category',
			'get'      => 'all',
			'slug'     => $leaf_path,
		)
	);

	if ( empty( $categories ) ) {
		return;
	}

	foreach ( $categories as $category ) {
		$path        = '/' . $leaf_path;
		$curcategory = $category;
		while ( ( 0 != $curcategory->parent ) && ( $curcategory->parent != $curcategory->term_id ) ) {
			$curcategory = get_term( $curcategory->parent, 'category' );

			if ( is_wp_error( $curcategory ) ) {
				return $curcategory;
			}

			$path = '/' . $curcategory->slug . $path;
		}

		if ( $path == $full_path ) {
			$category = get_term( $category->term_id, 'category', $output );
			_make_cat_compat( $category );

			return $category;
		}
	}

	// If full matching is not required, return the first cat that matches the leaf.
	if ( ! $full_match ) {
		$category = get_term( reset( $categories )->term_id, 'category', $output );
		_make_cat_compat( $category );

		return $category;
	}
}