The category attribute has changed in Divi 4.0, which is causing CSS to not be applied on archive and post pages. Replacing one word in Divi > Theme Options > Integration will resolve this issue.

In the jQuery added to Integration in Divi Theme Options, find the following section of code:

//Wrap the category in a container
$(".ds-blog .et_pb_post, .archive .et_pb_post, .search .et_pb_post, .single .et_pb_post").each(function () {
$(this).find('[rel~="category"]').wrapAll('<div class="ds-blog-cat"></div>');
//Move the vategory above the post title
$(this).find('.ds-blog-cat').detach().insertBefore($(".entry-title", this));
});


And change the rel~"category" to rel~"tag" so it should look like this:

//Wrap the category in a container
$(".ds-blog .et_pb_post, .archive .et_pb_post, .search .et_pb_post, .single .et_pb_post").each(function () {
$(this).find('[rel~="tag"]').wrapAll('<div class="ds-blog-cat"></div>');
//Move the vategory above the post title
$(this).find('.ds-blog-cat').detach().insertBefore($(".entry-title", this));
});

Save and your changes and the category will display correctly. Please be sure to clear any caches in your browser and/or at your web host.