How long do cats remember places and people? I will leave the house in the next months for half a year or so. Will my cat remember me when I get back?
Cats do remember places and people, although where/who they remember, and for how long, is variable (just like humans).
There's been some research on feline short-term memory, but I could find less information on long-term memory.
This article is rather poorly referenced, but does make some statements about long-term memory that it claims are research-based:
The inevitable anecdotes
I believe that I've experienced cats remembering me years after we have had prolonged interactions. One example is a roommate of mine that I lived with about 10 years ago. His cat is not generally friendly, but we got along very well, and I was one of the few people the cat would actively seek out (i.e. he would climb in my lap and sit there while I pet him). After my friend moved out, there were periods of 1-2 years in between my visits to his new home, and when I would come over, his cat would still come and climb in my lap for petting. Over times, my visits have unfortunately become less frequent (I moved out of the area), and while the cat still seems to remember me, he is not as friendly to me as he used to be.
Here is a video of someone who claims to have been reunited with their cat over a year after her cat left home and roamed the neighborhood as a feral cat:
The internet is littered with similar claims. There is also a host of unreferenced claims about feline memory that I won't include here.
However, it is pretty certain that your cat will remember you after 6 months if you interact with the cat on a regular basis.
Whether the cat is happy to see you (at first) will be another story... ours tend to seem mad at us when we come back after leaving for a few days, and we get the "cold shoulder" for the first day or so :)
I know cats have memory. I've known many cats in my life and often have observed that they "remember" me. I've seen this by cats acting a particular way to me versus other people. I knew this one cat in particular ("Maggie"), for most of her 22 year life (though I only had her for the last 7-8 years).
She would enjoy going into this ritual game/battle with me (and no one would see her do it with other people). She would get up on a surface that had cloth on it (like a bed, but sometimes a couch) and would furiously paw at it with her front paws. This would be my queue to pet her very fast on her sides, then she would flop over on her side and the game would begin.
My objective was to touch her whiskers or tummy and her objective was to bite me before I did this (she pulled her punches so she never broke the skin). She did this after one of the early times I met her and always did it with me, even though sometimes it was months or a year before I saw her again.
I'd agree with the statement that just like people their memories are variable. They tend to remember people and how the people treated them rather well.