How do we smoothly introduce our cats to the puppy?

[EmMcK]

We have two cats, 5 and 3, who have the run of the house and a cat door, so they come and go as they please but spend most of their time inside.
We are also getting a puppy (in 8 sleeps as the children would say) and I want to ask please for advice on how to introduce the three of them? The pup will be crate trained so I thought that I would set the crate up in the next couple of days - it is going to be in the living room - so the cats can get used to that, and then we are going to put in a baby gate so the cats can sidle through to the front of the house where the bedrooms are and where they spend the majority of their lives lolling around.
The pup will be 8 weeks old and has been socialised to cats, but the cats have always run a mile whenever anyone visits with a dog, so how do I keep them happy and make this a smooth transition?
TIA

You just let the cats decide really. If they appear, you reward the puppy generously for ignoring them, but don't do things like carrying a cat in to 'introduce' it to the puppy.
Some cats will take longer than others to settle down. One of mine rules the dogs (inc foster puppies) with an iron paw, the other took 2 years to accept the dogs. We have a baby gate on the kitchen so the cats can eat in peace, and access their cat flap. At night, and for young dogs, when we are out, the dogs are crated so the cats can have free run of the house in safety.

We just let them get on with it - while always making sure the cats had a dog free space.
One year on they don't totally hate him all the time!!

just as CMOT has said

do not allow the dog to harass the cats, let them set the pace. We've had lots of puppies through the place and the friendship mostly rests on how respectful the pup is

One of our cats would move upstairs until the other two had set the pace, of those two, one would treat all dogs with disdain and never miss an opportunity to stare and/or swipe and the other (idiotcat) would exercise his authority by forcing his way in to share the pup's food, or settling on its bed, or even trying to kiss the pup with a stern paw at the ready for any puppy shenanigans.

Two of the pups we had were really good friends with idiotcat, but mostly the others were just here.

I'd presume if your pup has been socialised already to a cat it will be relatively respectful rather than all out "ohmygod it's a floofy cat thing I must make it my friend" which never goes down well.

I let the cat and the puppy get on with it. IIRC the cat bashed the puppy on the nose once or twice, until the proper level of respect was attained, and now they get on beautifully - the cat comes to the dog for cuddles.

Sweet, this is what I was hoping I would hear. I suspect one cat will be permanently surprised by the puppy - he isn't the brightest and regularly forgets how to use the cat flap, while the other will take charge.
Am ludicrously excited about this puppy, we have been talking about getting one for a couple of years.

Yes, it is best to do everything at the cats pace. Make sure the cats always have an escape route or high place to get to to escape. It took my cat around 6 weeks to get to the stage where he was happy to sleep in the same room as the dog. They are still not bezzie mates, the cat thinks the dog is too annoying but they do not hate each other.