When I wake up, once I feel read for it, I just say "Goodmorning Banjo" and she will come and snuggle up to me for cuddles. Then the cat will join in. Not for smooching, but to attack the dog's wagging tail. Which makes me laugh. And the more I laugh, the more the dog wags her tail and the more frenzied the cat attacks it. Most of the time Banjo will ignore her. When the cat digs her nails or teeth in too much, she will just give her a pretend nip and go back to ignoring her.
Then I get up to get my coffee and feed the cat (I once left the kitchen without feeding her at this point and she ran after me and hung onto my ankle). Now the dog is lying on my feet with the cat snuggled up against her belly purring madly. This was after Banjo cleaned the cat's face to lick off any leftover cat food.
Banjo would get on with most cats. But this cat is very rapidly becoming a foster failure. I don't think I have the heart to rehome her anymore. She'd be fine adapting to new humans. It's the dog that she would miss like mad.