UPDATE: She still talks about her cat. It has evolved into spiders as well. She is psychotically fascinated with spiders, and will read off facts about them to me with almost no tone. This suits me as I do the same thing with weird animals I enjoy, although I usually do it very enthusiastically. I get less cat pictures than spider pictures, she sends compilations of spider pictures.
The original post was kind of half-joking, half serious. I really like talking to her, and we have a lot of weird interests in common. I just thought it was kind of funny/annoying that the conversation would occasionally halt so I could see pictures of her cat. My main problem is that I can't really say anything about her cat because it is just a cat. I have nothing to say about it that I didn't say a week ago, so I am left in an awkward position of not wanting to be a jerk and ignore the pictures, but also try and steer the conversation away from "that sure is a cat". The thing that has been most successful is to "run with the bit", that is comedically commenting on the picture and springboarding off of that into something different. Sometimes it just means more cat pictures.
I know a conversation should not be rocket science. I should not need a formula to redirect the dialogue towards human matters, but that is just how my brain works, and hers as well apparently. I have a close friend that I do this with, they will go silent for months, and if I want to ask them to hang out I need to either send a picture of an animal or a drawing I've done to get their attention. Once I identified this pattern it took the anxiety away from starting conversations, because I knew what to do to reliably get a response.
Everything I've spoken to her about that isn't cat related has been very interesting and stimulating, so for the most part the cat stuff does not bother me as much as it did a few days ago. She just really likes her cat.
Also: consider not being in constant text communication.
I think she doesn't have anyone to talk to. I wake up every morning with a new text from her, and the conversation usually continues all day. We are planning a get together for a movie night sort of thing next week, so god fucking willing this will not be a text based relationship forever.
Typing this out has made me realize I sound like an insane person. It's the cats, the cats did it to me.