I've been curious about the concept of categories in physics and tried finding some more information about the subject. There are lots of textbooks about category theory, some from mathematicians and some written specifically for physicists (example), but I'm having a hard time seeing in which areas of physics the topic comes up and how they are connected (if they are).
For example, I stumbled up on Topos Physics, which seems to make use of the language of categories. But I also saw something called "Categorical quantum mechanics", which seems to have relations to Category theory and Topos Physics. Category theory seems also to make an appearance in Quantum infromation theory (see here), so there seems to be once again a link to Topos Physics (over Catgeorical QM).
As mentioned above, I'm interested in the topic, but I'm only a graduate student (currently masters), whose studies up to now mostly focused on QFT, GR and Lie theory.
So my question boils down to:
- Does Category theory in physics mostly appear in connection to Topos Physics?
- Are there any topics close to QFT or GR that involve Category theory and are not completely off limits to a graduate student in physics (it seems that much of what I could find assumed extensive knowledge of String theory, which I don't have).
P.S. I saw this question, but I was hoping to find some more examples and maybe bit of a clearer structure in the overview.