I'm a undergrad student and I'm stidying most of this things on my own, or with help of some professors that are helping me a bit, just for fun and bulding a solid base for my future PHD, with I'm planig on doing on this area.
I want to study higher geometry, I'm quite familiar with category theory and I'm currently studying differential geometry and differential topology, also I know a bit about algebraic geometry and algebraic topology, not much, but I know schemes, some properties of they and their morphisms, also I will be starting to study cohomology soon.
My question is, after having a solid background on Algebraic Gemetry up to be really familiar with schemes and cohomology, be familiar with basic algebraic topology and having a solid knwoledg in differential geometry and differential topology, what should I study and by with sources like books, lecture notes and things like that?
I know that I will probably need to advence my studies in algebraic geometry up to a good understanding of stacks an all you can do with then and higher category theory, but what else whould I need to study and also, good sources for studying this topics are also welcome too.
I know my question is a little too broad, since higher geometry as a very broad subject and I will probably need to chose a part of it to focus my studies, but what I need is the background to start studying it, so I will be able to find the most interesting part of it for me and then focus on it.
And also a second question, I don't know if this is already entangled with higher geometry, but I couldn't find any source about higher topology, does this subject exist?
PS: Sorry for my english, my mother language is portuguese and I'm still learning english.