Log into the Commerce catalog. Then, navigate to the variant and click the Belongs to tab to see its path.

It is unclear what you are trying to do, but i assume you want to get the variant url

From the code you can use ReferenceConverter to get the content link

From the content link you can use UrlResolver.GetUrl to get the url of the content. In this case, the variant

We have created some EntryContentExtensions that will help you to retrieve the PrimaryCategory

public static NodeContent GetCategory(this EntryContentBase entryContent, IContentLoader contentLoader = null)
{
    return GetCategory<NodeContent>(entryContent, contentLoader);
}

Here is the method GetCategory<T>() definitions

public static T GetCategory<T>(this EntryContentBase entryContent, IContentLoader contentLoader = null)
    where T : NodeContent
{
    if (entryContent == null)
        return null;

    if (contentLoader == null)
    {
        contentLoader = ServiceLocator.Current.GetInstance<IContentLoader>();
    }

    var nodeContent = contentLoader
        .GetAncestors(entryContent.ContentLink)
        .FirstOrDefault(x => x is T);

    return nodeContent as T;
}

Let me know if it helps you.

Thanks

What you mentioned in the comment sounds like bread crumb. If that is the case, you can do like this https://leanpub.com/epicommercerecipes/read_sample (Recipe 1.9)