Hello,
The breadcrumb is build regarding the Joomla menu.
Since the carousel that you're referring too do not use a menu for the link ; there is no menu information.
So HikaShop can't know from where the customer is coming from, it cannot associate the breadcrumb with a menu ; it cannot know from which category it need to start the breadcrumb (because no menu and no configuration) and cannot generate the links for the categories (since it also require a menu).
That's why you can find in HikaShop modules some setting to force the usage of a specific menu while creating links for the products (or categories).
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.