We had an extended visit from

Pluto the cat yesterday.
Although he owns the humans on the corner of our short street he also visits our back garden almost daily. He may also visit other gardens. I do not know. Cats do not tell you such things.
Occasionally he will wander in and out of our house using our old cat flap.
Yesterday was cold and showery. Pluto strolled in just before lunch. He came and "talked" to me before settling himself in the windowsill. He then spent some time staring outside.
When we had eaten I looked to see if he was still in the window. No. Oh right, on the sofa.
He was tucked cosily between two cushions in a classic cat sleeping pose. He was curled in a little ball with his paw over his face and the tip of his tail resting on the tip of his nose. And that is where he stayed until late in the afternoon. Eventually he rose, cleaned himself (yet again) and left through the cat-flap.
My father and I are amused by this. Real cats (as opposed to the one who writes this blog) just move in. They take over. They invite themselves. They assume they are welcome. It is all so very different from the way in which humans normally behave.
What do cats think when they do this sort of thing -and how do they think it?